Question

when ms. shreve solved an equation in class, she checked her solution and it did not make the equation true! examine her work below and find her mistake. then find the correct solution. homework help
$5(2x - 1) - 3x = 5x + 9$
$10x - 5 - 3x = 5x + 9$
$7x - 5 = 5x + 9$
$12x = 4$
$x = \frac{1}{3}$

Explanation:

Step1: Identify the error

Ms. Shreve incorrectly combined $10x - 3x$ as $7x$, but then incorrectly rearranged terms: she should have moved $5x$ to the left and $-5$ to the right, but instead she subtracted $5x$ from the left incorrectly. First, start with the original equation:
$$5(2x - 1) - 3x = 5x + 9$$

Step2: Expand the left side

Distribute the 5 to the terms in parentheses:
$$10x - 5 - 3x = 5x + 9$$

Step3: Combine like terms on left

Combine $10x$ and $-3x$:
$$7x - 5 = 5x + 9$$

Step4: Isolate x terms on left

Subtract $5x$ from both sides:
$$7x - 5x - 5 = 9$$
$$2x - 5 = 9$$

Step5: Isolate the constant on right

Add 5 to both sides:
$$2x = 9 + 5$$
$$2x = 14$$

Step6: Solve for x

Divide both sides by 2:
$$x = \frac{14}{2}$$

Answer:

Ms. Shreve made an error when rearranging terms (she incorrectly calculated $7x - 5x$ as $12x$ instead of $2x$). The correct solution is $x=7$.