Solve the inequality: 7 > 5x - 13
Understand the Problem
The question is asking to solve an inequality for x. This requires isolating x on one side of the inequality to find the range of values that satisfy the given condition.
Answer
$x \leq 5$
Answer for screen readers
$x \leq 5$
Steps to Solve
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Isolate the term with $x$ We have the inequality $3x + 7 \leq 22$. To isolate the term with $x$, we subtract 7 from both sides of the inequality: $$3x + 7 - 7 \leq 22 - 7$$ $$3x \leq 15$$
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Solve for $x$ Now, to solve for $x$, we divide both sides of the inequality by 3: $$\frac{3x}{3} \leq \frac{15}{3}$$ $$x \leq 5$$
$x \leq 5$
More Information
The solution to the inequality $3x + 7 \leq 22$ is $x \leq 5$. This means that any value of $x$ less than or equal to 5 will satisfy the original inequality.
Tips
A common mistake is forgetting to flip the inequality sign when dividing or multiplying by a negative number. However, in this case, we divided by a positive number (3), so we don't need to flip the inequality sign. Another mistake is performing the arithmetic incorrectly when subtracting or dividing.
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