Question

question 2
for the following linear equation in the variable x, determine which of the follow
$5x - 7 = -12$
choose all that are correct.
subtract 5x from both sides
add 7 to both sides
add 12 to both sides
divide both sides by 0
divide both sides by 5

Explanation:

Step1: Analyze "Subtract 5x from both sides"

Subtracting \(5x\) from both sides of \(5x - 7=-12\) gives \(5x - 5x-7=-12 - 5x\), which simplifies to \(-7=-12 - 5x\). This does not help in solving for \(x\) directly, so this step is incorrect.

Step2: Analyze "Add 7 to both sides"

Adding 7 to both sides of \(5x - 7=-12\) gives \(5x-7 + 7=-12 + 7\), which simplifies to \(5x=-5\). This is a valid step in solving the linear equation.

Step3: Analyze "Add 12 to both sides"

Adding 12 to both sides of \(5x - 7=-12\) gives \(5x-7 + 12=-12 + 12\), which simplifies to \(5x + 5 = 0\). This is not a standard first step for solving \(5x-7=-12\) and complicates the process, so this step is incorrect.

Step4: Analyze "Divide both sides by 0"

Division by zero is undefined in mathematics, so this step is invalid.

Step5: Analyze "Divide both sides by 5"

After getting \(5x=-5\) (from adding 7 to both sides), dividing both sides by 5 gives \(\frac{5x}{5}=\frac{-5}{5}\), which simplifies to \(x = - 1\). This is a valid step in solving the linear equation.

Answer:

The correct options are:

• Add 7 to both sides
• Divide both sides by 5