Assignment: Solving a Difficult Two-Step Equation

Fill the empty slots by dragging tiles from the left to show the next step for solving the equation.

Solve the two-step equation:
[tex]\[ \frac{3}{4}x - 1.72 = -6.82 \][/tex]

1. The first step is to [tex]\(\square\)[/tex] on both sides.
2. The second step is to [tex]\(\square\)[/tex] on both sides.

The solution is [tex]\(x = \square\)[/tex]



Answer :

To solve the equation [tex]\(\frac{3}{4}x - 1.72 = -6.82\)[/tex], follow these detailed, step-by-step instructions:

1. The first step is to add 1.72 on both sides. This helps to isolate the term with [tex]\(x\)[/tex].

[tex]\[ \frac{3}{4}x - 1.72 + 1.72 = -6.82 + 1.72 \][/tex]

Simplifying both sides, we get:

[tex]\[ \frac{3}{4}x = -5.10 \][/tex]

2. The second step is to multiply by the reciprocal of [tex]\(\frac{3}{4}\)[/tex] on both sides. The reciprocal of [tex]\(\frac{3}{4}\)[/tex] is [tex]\(\frac{4}{3}\)[/tex].

[tex]\[ \left(\frac{4}{3}\right) \cdot \frac{3}{4}x = -5.10 \cdot \left(\frac{4}{3}\right) \][/tex]

Simplifying, we get:

[tex]\[ x = -6.8 \][/tex]

Therefore, the solution is [tex]\( x = -6.8 \)[/tex].