Fill in the blanks to follow the steps in solving the equation: 5x−12−6x=−10x+7−1
(4 points)
5x - 12 - 6x = -10x + 7 - 1
Combine like terms:
- x - 12 = - 10x + 6
Add 10x to both sides:
9x - 12 = 6
Add 12 to both sides:
9x = 18
Divide both sides by 9:
x = 2
Solving the inequality for x, which statement shows a good first step and which is the correct solution?
x−6<x4
(2 points)
Responses
Multiply both sides by x to get the "x" terms on the same side of the inequality: x−6<4
Multiply both sides by x to get the "x" terms on the same side of the inequality: x−6<4
Divide both sides of the inequality by x to simplify: 1−6x<4
x<6
Divide both sides of the inequality by x to simplify: 1−6x<4
x<6
Multiply both sides by 4 to clear the inequality of fractions: 4x−24<x
Multiply both sides by 4 to clear the inequality of fractions: 4x−24<x
Divide both sides of the inequality by 4 to simplify: x4−32<x
Divide both sides of the inequality by 4 to simplify: x4−32<x
Step 1: Arrange the equation so that all the variables are on one side and all the constants are on the other side.
- Starting equation: 5x - 12 - 6x = -10x + 7 - 1
- Rearrange the equation: 5x - 6x + 10x = 7 - 1 + 12
Step 2: Combine like terms on both sides.
- Simplify the terms on the left side: (-1x) + 10x = 9x
- Simplify the terms on the right side: 7 - 1 + 12 = 18
Step 3: Solve for x.
- Final equation: 9x = 18
- Divide both sides by 9 to solve for x: x = 18/9
- Simplify: x = 2
Therefore, the solution to the equation is x = 2.
To solve the given equation, we need to combine like terms on both sides of the equation. Let's fill in the blanks step by step:
1. First, let's combine like terms on the left side of the equation. We have 5x and -6x, so the sum of these terms is (5x - 6x) = -1x.
The equation now becomes:
-1x - 12 = -10x + 7 - 1.
2. Moving on to the right side of the equation, we have -10x, 7, and -1. The sum of 7 and -1 is (7 - 1) = 6.
The equation now becomes:
-1x - 12 = -10x + 6.
3. Next, we can combine like terms on the right side of the equation. We have -10x and 6, so the sum of these terms is (-10x + 6).
The equation now becomes:
-1x - 12 = -10x + 6.
4. Now, let's simplify the equation further. To do this, we can move all terms containing x to the left side of the equation and all constant terms to the right side.
Adding 10x to both sides of the equation:
-1x + 10x - 12 = -10x + 10x + 6.
9x - 12 = 6.
Adding 12 to both sides of the equation:
9x - 12 + 12 = 6 + 12.
9x = 18.
5. Finally, to solve for x, we divide both sides of the equation by 9:
(9x)/9 = 18/9.
x = 2.
Therefore, the solution to the equation is x = 2.