What is the solution to this equation?
$5(x-6)+3=-7$
A. $x=4$
B. $x=2$
C. $x=5$
D. $x=3$
Answer (1)
Distribute the 5: 5 ( x − 6 ) + 3 = 5 x − 30 + 3 .
Combine constant terms: 5 x − 27 = − 7 .
Add 27 to both sides: 5 x = 20 .
Divide both sides by 5: x = 4 . The solution is 4 .
Explanation
Problem Analysis We are given the equation 5 ( x − 6 ) + 3 = − 7 and asked to find the value of x that satisfies it. We will solve this equation step-by-step.
Distribute First, distribute the 5 into the parentheses: 5 ( x − 6 ) + 3 = 5 x − 30 + 3
Combine Constants Now, combine the constant terms on the left side of the equation: 5 x − 30 + 3 = 5 x − 27
Simplified Equation So, the equation becomes: 5 x − 27 = − 7
Isolate x Term Next, add 27 to both sides of the equation to isolate the term with x :
5 x − 27 + 27 = − 7 + 27
5 x = 20
Solve for x Finally, divide both sides by 5 to solve for x :
5 5 x = 5 20
x = 4
Verification To verify the solution, substitute x = 4 back into the original equation: 5 ( 4 − 6 ) + 3 = 5 ( − 2 ) + 3 = − 10 + 3 = − 7
Since the left side equals the right side, the solution is correct.
Final Answer Therefore, the solution to the equation 5 ( x − 6 ) + 3 = − 7 is x = 4 .
Examples
Linear equations are used in everyday life to calculate costs, distances, and other quantities. For example, if you want to buy a certain number of items at a store and you know the price per item and the total amount you can spend, you can use a linear equation to determine how many items you can buy. Suppose you have a budget of $50 and each item costs $5, and there is a fixed shipping fee of $5. The equation would be 5 x + 5 = 50 , where x is the number of items you can buy. Solving for x gives x = 9 , so you can buy 9 items.
