Break Compound Inequality: First, we will deal with the compound inequality by breaking it into two separate inequalities: 3x -1/2: Next, we divide both sides by -2 to solve for x. Remember that dividing by a negative number reverses the inequality sign. -2x / -2 > 1 / -2 x > -1/2Solve 5x + 1 -1/2 and x < 3. So, the final answer is -1/2 < x < 3.

Algebra 1

Solve two-step linear inequalities

Full solution

3x<5x+1<16

Break Compound Inequality: First, we will deal with the compound inequality by breaking it into two separate inequalities: 3x < 5x + 1 and 5x + 1 < 16.
Solve 3x < 5x + 1: Now, let's solve the first inequality 3x < 5x + 1. We will subtract $5x$ from both sides to isolate the variable on one side. $\newline$ 3x - 5x < 5x + 1 - 5x $\newline$ -2x < 1
Solve x > -\frac{1}{2}: Next, we divide both sides by $-2$ to solve for $x$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ -2x / -2 > 1 / -2 $\newline$ x > -\frac{1}{2}
Solve 5x + 1 < 16: Now, we will solve the second inequality 5x + 1 < 16. We will subtract $1$ from both sides to isolate the terms with $x$ . $\newline$ 5x + 1 - 1 < 16 - 1 $\newline$ 5x < 15
Solve x < 3: We divide both sides by $5$ to solve for $x$ .\frac{5x}{5} < \frac{15}{5}x < 3
Combine Inequalities: We now combine the results from the two inequalities to find the range of values for $x$ . The solution is the intersection of x > -\frac{1}{2} and x < 3. So, the final answer is -\frac{1}{2} < x < 3.