could someone please check these problems for me? Thank you!
1. -0.7x<-35
x<50
2. Solve by elimination
3x+4y=3
6x+8y=6
answer:0
3. find y intercept to graph
x+5y=10
answer: (0,2)(10,0)
4. use distributive law to solve
7(w-5)=-35
7w-35=-35
if i add 35 to both sides i get 0
5. Simplify
1[-61-(58-85)]
1[-61-(-27)]
1[-61+27]
-61+27
-34
1. Doesn't the inequality sign change directions when you divide by a - sign?
2. The lines are the same, no solution.
3. the y intercept is 2. I am not certain why you provide the other information.
4, 5 correct
When you multiply or divide an inequality by a negative number, change the direction of the arrow
1. -0.7x<-35
x>50
1. To solve the inequality -0.7x < -35, we want to isolate the variable x. First, we divide both sides of the inequality by -0.7 (since we want to isolate x, we divide by the coefficient of x). However, we must be careful when dividing by a negative number because that will change the direction of the inequality.
Therefore, the correct step is to divide both sides by -0.7 while also flipping the direction of the inequality. This gives us x > 50. So the correct solution is x < 50.
2. To solve the system of equations using elimination, we want to eliminate one variable by adding or subtracting the equations. In this case, we can multiply the first equation by 2 and the second equation by 3 to get:
6x + 8y = 6 (multiplied first equation by 2)
6x + 8y = 6 (multiplied second equation by 3)
This means the two equations are identical, and they represent the same line. Therefore, there are infinitely many solutions. In other words, every point on the line (3x + 4y = 3) is a solution.
3. To find the y-intercept for the equation x + 5y = 10, we set x = 0 and solve for y. By substituting x = 0 into the equation, we get:
0 + 5y = 10
5y = 10
y = 2
So the y-intercept is (0, 2). Additionally, we can set y = 0 and solve for x to find the x-intercept. By substituting y = 0 into the equation, we get:
x + 5(0) = 10
x = 10
So the x-intercept is (10, 0). Therefore, the correct answer is (0, 2) and (10, 0).
4. To solve the equation 7(w-5) = -35 using the distributive law, we distribute 7 to both terms inside the parentheses. This gives us:
7w - 35 = -35
To isolate w, we add 35 to both sides of the equation:
7w - 35 + 35 = -35 + 35
7w = 0
So the solution is 7w = 0, which simplifies to w = 0.
5. To simplify the expression 1[-61-(58-85)], we start by evaluating the expression inside the innermost parentheses:
58 - 85 = -27
Next, we simplify the expression -61 - (-27):
-61 - (-27) = -61 + 27 = -34
Finally, we multiply by 1:
1 * (-34) = -34
So the simplified expression is -34.