1. Is the equation true, false, or open?
4y + 8 = 6y + 3 (1 point)
True; the expressions are the same for all values of the variables.
False; the expressions are never the same.
Open; there is a variable.
2. Which value is a solution of the equation 5 – 4x = –3? (1 point)
0
2
–3
one fourth
3. Which ordered pair is a solution of the equation y = x – 3? (1 point)
(–2, 5)
(–5, 2)
(2, 5)
(5, 2)
4. Which ordered pair is a solution of the equation y = 5x? (1 point)
(–2, 10)
(–5, 25)
(–3, 15)
(–2, –10)
5. Which ordered pair is a solution of the equation y = –7x + 2? (1 point)
(1, 2)
(8, –54)
(5, –35)
(1, –7)
6. Nick and his cousin Sara have the same birthday, but Nick is four years older than Sara. Let the variable x represent Nick’s age and y represent Sara’s age. Which graph represents the relationship between Nick’s age and Sara’s age? (1 point)
The first quadrant of a coordinate plane titled “Nick’s and Sara’s Ages” is shown. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 0 comma 4 right parenthesis, left parenthesis 2 comma 6 right parenthesis, and left parenthesis 4 comma 8 right parenthesis.
The first quadrant of a coordinate plane titled “Nick’s and Sara’s Ages” is shown. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 0 comma 0 right parenthesis, left parenthesis 4 comma one-half right parenthesis, and left parenthesis 8 comma 1 right parenthesis.
The first quadrant of a coordinate plane titled “Nick’s and Sara’s Ages” is shown. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 0 comma 0 right parenthesis, left parenthesis one-half comma 4 right parenthesis, and left parenthesis 1 comma 8 right parenthesis.
The first quadrant of a coordinate plane titled “Nick’s and Sara’s Ages” is shown. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 4 comma 0 right parenthesis, left parenthesis 6 comma 2 right parenthesis, and left parenthesis 8 comma 4 right parenthesis.
7. Solve the following equation.
–5 = x + 3 (1 point)
x = 2
x = –2
x = 8
x = –8
8. Solve the following equation.
x – 3 = –5 (1 point)
x = The fraction is negative 5 over 3.
x = –2
x = –8
x = 15
9. Solve the following equation.
2.8 = 2y (1 point)
y = 1.4
y = one half
y = 2.8
y = 0.6
10. Solve the following equation.
–9 = Start Fraction r over 4 End Fraction (1 point)
r = 36
r = 13
r =nine-fourths
r = –36
11. Solve the following equation.
–4 = seven over thirty-three times x (1 point)
x = one hundred thirty two over seven
x = Negative one hundred thirty two over seven
x = Negative seven over one hundred thirty two
x = Negative thirty three over twenty eight
12. Which equation is an identity? (1 point)
7 – (9x + 3) = –9x – 4
6m – 5 = 7m + 5 – m
10p + 6 – p = 12p – 3(p – 2)
3y + 2 = 3y – 2
13. Which equation has no solution? (1 point)
5 m minus 6 equals 5 m plus 7 minus m
3 w plus 4 minus w equals 5 w minus 2 left parenthesis w minus 2 right parenthesis
7 y plus 9 equals 7 y minus 6
4 z plus 8 equals negative 4 z minus 2
14. Solve the following equation.
3(x – 7) – x = 2x – 21 (1 point)
7
–2
infinitely many solutions
no solution
15. Solve the following equation.
3 + 6z = 13 + 6z (1 point)
z = –
z = 2two-thirds
infinitely many solutions
no solution
16. Ella and Margaret were at a carnival. They each got a ticket for the Ferris wheel. Ella got a snow cone, and Margaret got a cotton candy. Ella had a certificate for $6 off the cost. Margaret paid the rest, which came to $12.75. Each Ferris wheel ticket was $5, and a snow cone was $3.50. What was the cost for cotton candy? (1 point)
$5.00
$5.25
$2.50
$7.25
17. Solve the following equation.
3(y – 5) + 2 = 5 (1 point)
y = 4
y = 7
y = –4
y = 6
18. Solve the following equation.
70 = –7(–2 – 2z) (1 point)
z = 4
z = –28
z = –112
z = 784
19. Solve the following equation.
–4y + 8 = 4(2y – 2) – 2(–16 + 8y) (1 point)
y = –4
y = 4
y = –2
y = –6
any ideas, or is this just a homework dump?
I'll do one.
-4y+8 = 4(2y-2) - 2(-16+8y)
-4y+8 = 8y-8 - (-32+16y)
-4y+8 = 8y-8+32-16y
-4y-8y+16y = -8+32-8
4y = 16
y = 4
righttt
1. The equation is true; the expressions are the same for all values of the variables.
2. The solution to the equation 5 - 4x = -3 is x = 2.
3. The ordered pair (2, 5) is a solution of the equation y = x - 3.
4. The ordered pair (-2, 10) is a solution of the equation y = 5x.
5. The ordered pair (1, 2) is a solution of the equation y = -7x + 2.
6. The graph that represents the relationship between Nick's age and Sara's age is the one that passes through the points (0, 4), (2, 6), and (4, 8).
7. The solution to the equation -5 = x + 3 is x = -8.
8. The solution to the equation x - 3 = -5 is x = -2.
9. The solution to the equation 2.8 = 2y is y = 1.4.
10. The solution to the equation -9 = (r/4) is r = -36.
11. The solution to the equation -4 = (7/33)x is x = -132/7.
12. The equation 3y + 2 = 3y - 2 is an identity.
13. The equation 4z + 8 = -4z - 2 has no solution.
14. The solution to the equation 3(x - 7) - x = 2x - 21 is x = 7.
15. The equation 3 + 6z = 13 + 6z has no solution.
16. The cost for cotton candy is $7.25.
17. The solution to the equation 3(y - 5) + 2 = 5 is y = 4.
18. The solution to the equation 70 = -7(-2 - 2z) is z = 4.
19. The solution to the equation -4y + 8 = 4(2y - 2) - 2(-16 + 8y) is y = 4.
1. The equation 4y + 8 = 6y + 3 is open because there is a variable present (y) and it is not specified if the equation is true or false for all values of y.
2. To find the solution to the equation 5 - 4x = -3, you can solve for x by isolating the variable. Begin by subtracting 5 from both sides of the equation to get -4x = -8. Then, divide both sides by -4, which gives you x = 2. Therefore, the value 2 is a solution to the equation.
3. To determine which ordered pair is a solution of the equation y = x - 3, substitute the values of the ordered pairs into the equation and see if the equation holds true. The only ordered pair that satisfies the equation is (-2, 5). Therefore, (-2, 5) is the solution to the equation.
4. Similar to the previous question, you need to substitute the values of the ordered pair into the equation y = 5x. The only ordered pair that satisfies the equation is (-2, 10). Thus, (-2, 10) is the solution to the equation.
5. Again, substitute the values of the ordered pair into the equation y = -7x + 2. The only ordered pair that satisfies the equation is (1, 2). So, (1, 2) is the solution to the equation.
6. Since Nick is four years older than Sara, the relationship between their ages can be represented by a linear equation y = x - 4. The graph that represents this equation is the first quadrant of a coordinate plane titled "Nick's and Sara's Ages", and it shows a line passing through the points (0, 4), (2, 6), and (4, 8). Therefore, the correct graph is the first option.
7. To solve the equation -5 = x + 3, subtract 3 from both sides to get x = -8. Thus, the solution to the equation is x = -8.
8. To solve the equation x - 3 = -5, add 3 to both sides to get x = -2. Therefore, x = -2 is the solution to the equation.
9. To solve the equation 2.8 = 2y, divide both sides by 2 to get y = 1.4. Hence, the solution to the equation is y = 1.4.
10. To solve the equation -9 = r/4, multiply both sides by 4 to get r = -36. Thus, the solution to the equation is r = -36.
11. To solve the equation -4 = (7/33)x, multiply both sides by 33/7. This gives x = -132/7, which simplifies to x = -18 6/7. Therefore, the solution to the equation is x = -18 6/7.
12. An identity equation is true for all values of the variable. Among the given equations, the only one that meets this condition is 3y + 2 = 3y - 2. Therefore, 3y + 2 = 3y - 2 is an identity equation.
13. To determine which equation has no solution, analyze each equation. The equation 7y + 9 = 7y - 6 leads to a false statement (9 = -6) and it cannot be true for any value of y. Hence, 7y + 9 = 7y - 6 has no solution.
14. Solve the equation 3(x - 7) - x = 2x - 21 by first distributing the 3 and simplifying: 3x - 21 - x = 2x - 21. Simplifying further, 2x - 21 = 2x - 21. In this case, the equation is an identity equation, which means it is true for all values of x. Therefore, this equation has infinitely many solutions.