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Solved on Dec 08, 2023

Solve linear equations with one variable. Click to show solutions for -75, -3, and other values.

STEP 1

Assumptions
1. We have three equations to solve: x5=−15\frac{x}{5}=-15, 5x=−155x=-15, and −5x=−15-5x=-15.
2. We need to determine the solution for each equation.
3. The solution to each equation will be marked with a check (✓) in the corresponding box under the correct number in the table.

STEP 2

Solve the first equation x5=−15\frac{x}{5}=-15.
Multiply both sides of the equation by 5 to isolate xx.
5⋅x5=5⋅(−15)5 \cdot \frac{x}{5} = 5 \cdot (-15)

STEP 3

Simplify the equation by canceling out the 5 on the left side and multiplying 5 by -15 on the right side.
x=−75x = -75

STEP 4

Mark the solution in the table. The solution to x5=−15\frac{x}{5}=-15 is x=−75x=-75. We will place a check (✓) in the box under -75 for the first equation.
\begin{tabular}{|c|c|c|c|c|} \hline & -75 & -3 & & \\ \hlinex5=−15\frac{x}{5}=-15 & ✓ & □\square & L & \\ \hline 5x=−155 x=-15 & □\square & 0 & □\square & \\ \hline−5x=−15-5 x=-15 & □\square & 口 & □\square & \\ \hline \end{tabular}

STEP 5

Solve the second equation 5x=−155x=-15.
Divide both sides of the equation by 5 to isolate xx.
5x5=−155\frac{5x}{5} = \frac{-15}{5}

STEP 6

Simplify the equation by canceling out the 5 on the left side and dividing -15 by 5 on the right side.
x=−3x = -3

STEP 7

Mark the solution in the table. The solution to 5x=−155x=-15 is x=−3x=-3. We will place a check (✓) in the box under -3 for the second equation.
\begin{tabular}{|c|c|c|c|c|} \hline & -75 & -3 & & \\ \hlinex5=−15\frac{x}{5}=-15 & ✓ & □\square & L & \\ \hline 5x=−155 x=-15 & □\square & ✓ & □\square & \\ \hline−5x=−15-5 x=-15 & □\square & 口 & □\square & \\ \hline \end{tabular}

STEP 8

Solve the third equation −5x=−15-5x=-15.
Divide both sides of the equation by -5 to isolate xx.
−5x−5=−15−5\frac{-5x}{-5} = \frac{-15}{-5}

STEP 9

Simplify the equation by canceling out the -5 on the left side and dividing -15 by -5 on the right side.
x=3x = 3

STEP 10

Since the solution x=3x=3 is not listed in the table, we will not place a check (✓) in any of the boxes for the third equation. Instead, we will mark the box under the empty column for the third equation.
\begin{tabular}{|c|c|c|c|c|} \hline & -75 & -3 & & \\ \hlinex5=−15\frac{x}{5}=-15 & ✓ & □\square & L & \\ \hline 5x=−155 x=-15 & □\square & ✓ & □\square & \\ \hline−5x=−15-5 x=-15 & □\square & 口 & ✓ & \\ \hline \end{tabular}
The table is now complete with the solutions marked for each equation.

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