Solve the inequality: 5x + 7 > 3(x + 1)
Understand the Problem
The question is asking to solve the inequality for x. We need to isolate x to find the range of values that satisfy the inequality. The steps typically involve distributing, combining like terms, and then isolating x.
Answer
$x > -2$
Answer for screen readers
$x > -2$
Steps to Solve
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Distribute the 3 on the right side of the inequality Multiply 3 by both $x$ and 1 inside the parentheses. $$ 5x + 7 > 3x + 3 $$
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Subtract $3x$ from both sides This will move the $x$ terms to the left side. $$ 5x - 3x + 7 > 3x - 3x + 3 $$ $$ 2x + 7 > 3 $$
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Subtract 7 from both sides This will isolate the $x$ term on the left side. $$ 2x + 7 - 7 > 3 - 7 $$ $$ 2x > -4 $$
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Divide both sides by 2 This will solve for $x$. $$ \frac{2x}{2} > \frac{-4}{2} $$ $$ x > -2 $$
$x > -2$
More Information
The solution to the inequality $5x + 7 > 3(x + 1)$ is $x > -2$. This means any value of $x$ greater than -2 will satisfy the original inequality.
Tips
A common mistake is forgetting to distribute the 3 to both terms inside the parenthesis on the right side of the inequality. Another common mistake is not flipping the inequality sign when multiplying or dividing by a negative number, but in this case, we did not multiply or divide by a negative number.
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