Solve negative 2 times y plus seven fifths times y equals negative 4 minus three fifths times y minus 2 for y.
a) y = 0
b) y = −13
c) No solution
d) Infinite solutions
To solve the equation, we can combine like terms and isolate the variable y on one side of the equation.
Starting with the given equation:
-2y + (7/5)y = -4 - (3/5)y - 2
Multiplying 7/5 and y, we get:
(-2 + 7/5)y = -4 - (3/5)y - 2
Combining the fractions, we have:
(-2 + 7/5)y = -4 - 3/5y - 2
Finding a common denominator of 5, the equation becomes:
(-10/5 + 7/5)y = (-20/5 - 3/5y - 10/5)
Simplifying the equation further:
(-3/5)y = (-33/5 - 3/5y)
Multiplying each side by 5 to eliminate the fraction:
-3y = -33 - 3y
We can see that the variable y cancels out on both sides, which means the equation simplifies to:
0 = -33
This statement is false, so there is NO SOLUTION to the given equation.
Therefore, the correct answer is:
c) No solution
Rewrite 5x + 25 using a common factor.
a) 5(x + 5)
b) 5(x + 25)
c) 5x(x + 5)
d) 5x(x + 25)
To rewrite 5x + 25 using a common factor, we can factor out 5 from both terms.
Taking out the common factor 5, we have:
5(x + 5)
Therefore, the correct answer is:
a) 5(x + 5)
Simplify −7g(2g + 3).
a) −14g2 − 21g
b) −14g2 + 3
c) −14g − 21g
d) −14g + 3
To simplify −7g(2g + 3), we need to apply the distributive property.
Multiplying −7g by 2g gives us −14g², and multiplying −7g by 3 gives us −21g.
Putting it all together, we have:
−7g(2g + 3) = −14g² − 21g
Therefore, the correct answer is:
a) −14g² − 21g
Multiply 2.9x and 5x.
a) 14.5x2
b) 7.9x2
c) 14.5x
d) 7.9x
To multiply 2.9x and 5x, we can simplify the expression by multiplying the coefficients and adding the exponents of the variables.
2.9 x 5 = 14.5
x^1 x x^1 = x^2
Putting it all together, we have:
2.9x * 5x = 14.5x^2
Therefore, the correct answer is:
a) 14.5x^2
Solve the equation for w.
2w + 6 + 0.3w = −0.7w − 12
a) w = 6
b) w = 0
c) w = −6
d) No solution
To solve the equation 2w + 6 + 0.3w = -0.7w - 12 for w, we can start by combining like terms on both sides of the equation.
On the left side of the equation, we can add 2w and 0.3w:
2w + 0.3w = 2.3w
On the right side of the equation, we can add -0.7w and -12:
-0.7w - 12 = -0.7w - 12
The equation now becomes:
2.3w + 6 = -0.7w - 12
To isolate the variable w on one side, we can subtract 2.3w from both sides:
2.3w - 2.3w + 6 = -2.3w - 2.3w - 12
6 = -2.3w - 2.3w - 12
Simplifying further:
6 = -4.6w - 12
Next, we can add 12 to both sides:
6 + 12 = -4.6w - 12 + 12
18 = -4.6w
To solve for w, divide both sides of the equation by -4.6:
18 / -4.6 = -4.6w / -4.6
-3.913 = w
Therefore, the solution to the equation is:
w = -3.913, which is approximately equal to -4
So, the correct answer is:
d) No solution
Solve the inequality and graph the solution.
−0.8b + 2.3 ≥ 8.7
a) number line with an open circle plotted at negative eight and arrow pointing right
b) number line with a closed circle plotted at negative eight and arrow pointing right
c) number line with an open circle plotted at negative eight and arrow pointing left
d) number line with a closed circle plotted at negative eight and arrow pointing left