Question:
If \(5(3x + y) = 15\), what is x in terms of y?
If \(5(3x + y) = 15\), what is x in terms of y?
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After you've isolated the variable, your answer might not look exactly like the multiple-choice options. Be prepared to simplify or rearrange your result, for example by splitting a fraction into two parts as shown in the solution.
Updated On: Oct 3, 2025
- \(x = 10 - \frac{y}{3}\)
- \(x = 3 - 3y\)
- \(x = 10 + \frac{y}{3}\)
- \(x = 15 + \frac{5y}{3}\)
- \(x = 1 - \frac{y}{3}\)
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Solution and Explanation
Step 1: Understanding the Concept:
"Expressing x in terms of y" means rearranging the given equation to isolate x on one side, with the other side containing only y and constants.
Step 2: Key Formula or Approach:
We will use algebraic manipulation to solve the equation for x.
Step 3: Detailed Explanation:
The given equation is: \[ 5(3x + y) = 15 \] First, divide both sides by 5 to simplify the equation: \[ 3x + y = \frac{15}{5} \] \[ 3x + y = 3 \] Next, subtract y from both sides to isolate the term with x: \[ 3x = 3 - y \] Finally, divide both sides by 3 to solve for x: \[ x = \frac{3 - y}{3} \] This can be split into two fractions: \[ x = \frac{3}{3} - \frac{y}{3} \] \[ x = 1 - \frac{y}{3} \] Step 4: Final Answer:
In terms of y, x is \(1 - \frac{y}{3}\).
"Expressing x in terms of y" means rearranging the given equation to isolate x on one side, with the other side containing only y and constants.
Step 2: Key Formula or Approach:
We will use algebraic manipulation to solve the equation for x.
Step 3: Detailed Explanation:
The given equation is: \[ 5(3x + y) = 15 \] First, divide both sides by 5 to simplify the equation: \[ 3x + y = \frac{15}{5} \] \[ 3x + y = 3 \] Next, subtract y from both sides to isolate the term with x: \[ 3x = 3 - y \] Finally, divide both sides by 3 to solve for x: \[ x = \frac{3 - y}{3} \] This can be split into two fractions: \[ x = \frac{3}{3} - \frac{y}{3} \] \[ x = 1 - \frac{y}{3} \] Step 4: Final Answer:
In terms of y, x is \(1 - \frac{y}{3}\).
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