Question:
Solve \( 6(2x+3) + x>53 - 2x \).
Solve \( 6(2x+3) + x>53 - 2x \).
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When solving inequalities, treat them like equations, but remember to reverse the inequality sign when multiplying or dividing by a negative number.
Updated On: Apr 18, 2026
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Solution and Explanation
Step 1: Expand the equation.
Distribute the 6 on the left-hand side: \[ 6(2x + 3) = 12x + 18 \] So the inequality becomes: \[ 12x + 18 + x>53 - 2x \]
Step 2: Simplify the inequality.
Combine like terms: \[ 13x + 18>53 - 2x \]
Step 3: Move all terms involving \( x \) to one side.
Add \( 2x \) to both sides: \[ 15x + 18>53 \]
Step 4: Solve for \( x \).
Subtract 18 from both sides: \[ 15x>35 \] Now, divide by 15: \[ x>\frac{35}{15} = \frac{7}{3} \]
Step 5: Conclusion.
The solution to the inequality is: \[ x>\frac{7}{3} \]
Distribute the 6 on the left-hand side: \[ 6(2x + 3) = 12x + 18 \] So the inequality becomes: \[ 12x + 18 + x>53 - 2x \]
Step 2: Simplify the inequality.
Combine like terms: \[ 13x + 18>53 - 2x \]
Step 3: Move all terms involving \( x \) to one side.
Add \( 2x \) to both sides: \[ 15x + 18>53 \]
Step 4: Solve for \( x \).
Subtract 18 from both sides: \[ 15x>35 \] Now, divide by 15: \[ x>\frac{35}{15} = \frac{7}{3} \]
Step 5: Conclusion.
The solution to the inequality is: \[ x>\frac{7}{3} \]
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