Which value of $x$ makes this equation true
$-8(x+5)=-3 x-7+x-3$
A. $x=-7 \frac{1}{2}$
B. $x=-5$
C. $x=1 \frac{1}{4}$
D. $x=12$
Answer (1)
Expand the left side of the equation: − 8 ( x + 5 ) = − 8 x − 40 .
Simplify the right side of the equation: − 3 x − 7 + x − 3 = − 2 x − 10 .
Rewrite the equation as − 8 x − 40 = − 2 x − 10 .
Solve for x : x = − 5 .
The value of x that makes the equation true is − 5 .
Explanation
Problem Analysis We are given the equation − 8 ( x + 5 ) = − 3 x − 7 + x − 3 and asked to find the value of x that makes the equation true. We will solve this equation by simplifying both sides and isolating x .
Expanding the Left Side First, we expand the left side of the equation by distributing the − 8 to both terms inside the parentheses: − 8 ( x + 5 ) = − 8 x − 40 .
Simplifying the Right Side Next, we simplify the right side of the equation by combining like terms: − 3 x − 7 + x − 3 = ( − 3 x + x ) + ( − 7 − 3 ) = − 2 x − 10 .
Rewriting the Equation Now we rewrite the equation with the simplified expressions: − 8 x − 40 = − 2 x − 10 .
Adding 8x to Both Sides To isolate x , we first add 8 x to both sides of the equation: − 8 x − 40 + 8 x = − 2 x − 10 + 8 x , which simplifies to − 40 = 6 x − 10 .
Adding 10 to Both Sides Next, we add 10 to both sides of the equation: − 40 + 10 = 6 x − 10 + 10 , which simplifies to − 30 = 6 x .
Dividing by 6 Finally, we divide both sides of the equation by 6 to solve for x : 6 − 30 = 6 6 x , which simplifies to x = − 5 .
Final Answer Therefore, the value of x that makes the equation true is x = − 5 .
Examples
Solving linear equations like this is a fundamental skill in algebra and is used in many real-world applications. For example, suppose you are trying to determine how many hours you need to work at a job that pays $15 per hour to buy a new phone that costs $600. You could set up an equation to represent this situation and solve for the number of hours. Similarly, in physics, you might use linear equations to calculate the distance an object travels at a constant speed over a certain amount of time. Understanding how to solve these equations allows you to model and solve a wide range of problems in various fields.
