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21 < 5x+1 > 6x-7

$21<5 x+1>6 x-7$

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Solve multi-step inequalities

Full solution

Q.

21<5 x+1>6 x-7

Isolate middle term: First, let's isolate the middle term by subtracting $1$ from all three parts of the inequality. $21 - 1 < 5x + 1 - 1 > 6x - 7 - 1$ $20 < 5x > 6x - 8$
Deal with left part: Now, let's deal with the left part of the inequality. $\newline$ $20 < 5x$ $\newline$ Divide both sides by $5$ to solve for $x$ . $\newline$ $\frac{20}{5} < \frac{5x}{5}$ $\newline$ $4 < x$
Handle right part: Next, let's handle the right part of the inequality. $\newline$ $5x > 6x - 8$ $\newline$ Subtract $6x$ from both sides. $\newline$ $5x - 6x > -8$ $\newline$ $-x > -8$
Divide by $-1$ : Now, we need to divide by $-1$ , remembering that this reverses the inequality sign. $\frac{-x}{-1} < \frac{-8}{-1}$ $x < 8$
Combine parts: Combine the two parts of the inequality to get the solution. $4 < x < 8$

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