Next step for solving the equation.
$\frac{3}{4}(x)-1.72=-6.82$
1. The first step is to $\square$ on both sides.
2. The second step is to $\square$ on both sides.
The solution is $x=$ $\square$
Answer (1)
Add 1.72 to both sides of the equation to isolate the term with x : 4 3 x = − 5.1 .
Multiply both sides of the equation by 3 4 to solve for x : x = 3 4 ( − 5.1 ) .
Simplify the expression to find the value of x : x = − 6.8 .
The solution to the equation is − 6.8 .
Explanation
Isolating the x term We are given the equation 4 3 ( x ) − 1.72 = − 6.82 and asked to solve for x . Our first goal is to isolate the term containing x , which is 4 3 x . To do this, we need to eliminate the − 1.72 on the left side of the equation. We can accomplish this by adding 1.72 to both sides of the equation.
Adding 1.72 to both sides Adding 1.72 to both sides of the equation, we get: 4 3 x − 1.72 + 1.72 = − 6.82 + 1.72 4 3 x = − 5.1
Isolating x Now that we have 4 3 x = − 5.1 , we need to isolate x . Since x is multiplied by 4 3 , we can isolate x by multiplying both sides of the equation by the reciprocal of 4 3 , which is 3 4 .
Multiplying by the reciprocal Multiplying both sides by 3 4 , we get: 3 4 ⋅ 4 3 x = 3 4 ⋅ ( − 5.1 ) x = 3 4 ⋅ ( − 5.1 ) x = − 6.8
Final Answer Therefore, the solution to the equation is x = − 6.8 .
Examples
Imagine you're trying to figure out how many hours you need to work this week to buy a new video game. You know that \frac{3}{4} of your hourly wage, after some deductions, minus $1.72 in taxes per hour, needs to equal -$6.82 (since you're starting in debt). Solving this equation helps you determine the exact number of hours you need to work to afford that game. This kind of problem applies to budgeting, figuring out work hours, or any situation where you need to solve for an unknown quantity in a linear equation.
