Put the steps in order for solving the equation: −2(4x+8)+2x = −5x+10
(1 point)
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1) Distribute the negative sign to both terms inside the parentheses: -8x - 16 + 2x = -5x + 10
2) Combine like terms on both sides of the equation: -6x - 16 = -5x + 10
3) Add 5x to both sides of the equation: -6x - 5x - 16 = 10
4) Combine like terms on the left side of the equation: -11x - 16 = 10
5) Add 16 to both sides of the equation: -11x = 26
6) Divide both sides of the equation by -11 to solve for x: x = -26/11
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A student wants to purchase some new school supplies. He wants to buy a calculator that costs $24 and some notebooks for school. Each notebook costs $2. The student only has $37 to spend.
Let n represent the number of notebooks that he buys.
Which inequality describes this scenario?
(1 point)
Responses
37≥2n+24
37 is greater than or equal to 2 n plus 24
24n+2≥37
24 n plus 2 is greater than or equal to 37
37>2n+24
37 is greater than 2 n plus 24
37<2n+24
1. Distribute the -2 to the terms inside the parentheses: -8x - 16 + 2x = -5x + 10
2. Combine like terms on both sides of the equation: -6x - 16 = -5x + 10
3. Add 5x to both sides of the equation: -x - 16 = 10
4. Add 16 to both sides of the equation: -x = 26
5. Multiply both sides of the equation by -1: x = -26
To solve the equation −2(4x+8)+2x = −5x+10, follow these steps:
1. Distribute the -2 to the terms inside the parentheses:
-2 * 4x = -8x
-2 * 8 = -16
The equation becomes: -8x - 16 + 2x = -5x + 10
2. Combine like terms on each side of the equation:
(-8x + 2x) - 16 = -5x + 10
-6x - 16 = -5x + 10
3. Move all the terms with x to one side of the equation by adding 6x to both sides:
-6x + 6x - 16 = -5x + 6x + 10
-16 = x + 10
4. Move the constant term to the other side of the equation by subtracting 10 from both sides:
-16 - 10 = x + 10 - 10
-26 = x
5. Simplify the solution:
x = -26
Therefore, the solution to the equation −2(4x+8)+2x = −5x+10 is x = -26.