Question

When ms. shreve solved an equation in class, she checked her solution and found that it did not make the equation true! Examine her work below and find her mistake. Then find the correct solution.

5(2×-1)-3×=5×+9
10×-5-3×=5×+9
7×-5=5××9
12×=4
×=1/3

Answer 1

Ms. Shreve made a mistake in combining like terms and applying the correct operations. The proper steps reveal that the correct solution to the equation 5(2x-1) - 3x = 5x + 9 is x = 7.

Step-by-step explanation:

When analyzing the equation 5(2x-1) - 3x = 5x + 9, we can check the solution step by step:

• Distribute the 5 in the parentheses: 5 * 2x gives 10x, and 5 * -1 gives -5. The equation becomes 10x - 5 - 3x = 5x + 9.
• Combine like terms on the left side: 10x - 3x gives 7x, so we get 7x - 5 = 5x + 9.
• To isolate the x terms on one side, subtract 5x from both sides: 7x - 5x - 5 = 9. This reduces to 2x - 5 = 9.
• Add 5 to both sides to solve for 2x: 2x = 14.
• Divide both sides by 2 to find x: x = 7.

Ms. Shreve made a mistake when she wrote 7x - 5 = 5x + 9 as 12x = 4. This step disregards the proper rules of combining like terms and the correct operations of subtraction and addition. The correct steps lead to the solution x = 7, which can be checked by substituting back into the original equation.

Answer 2

The first part of the second line, she left the -5 there. The correct work and solution should be this:
5(2x-1)-3x=5x+9
7x−5=5x+9
2x-5=9
2x=14
x=7