Multiple Choice
Write the following in interval notation.
2. Linear Equations and Inequalities
Linear Inequalities in One Variable
Multiple Choice
Solve the following linear inequalities using the addition and subtraction properties of equality.
A
B
C
D
Verified step by step guidance1
Start with the given inequality: \(7x + 3 < 2x + 13\).
Use the subtraction property of inequality to get all terms involving \(x\) on one side. Subtract \$2x$ from both sides: \(7x - 2x + 3 < 2x - 2x + 13\), which simplifies to \(5x + 3 < 13\).
Next, isolate the term with \(x\) by subtracting 3 from both sides: \(5x + 3 - 3 < 13 - 3\), which simplifies to \(5x < 10\).
Now, solve for \(x\) by dividing both sides by 5 (note that since 5 is positive, the inequality direction remains the same): \(\frac{5x}{5} < \frac{10}{5}\), which simplifies to \(x < 2\).
The solution to the inequality is \(x < 2\), meaning all values of \(x\) less than 2 satisfy the original inequality.
Related Videos
Related Practice