How do you solve #\frac { 3} { 4} \leq x - \frac { 7} { 8}

Question

How do you solve #\frac { 3} { 4} \leq x - \frac { 7} { 8} < \frac { 5} { 6}#?

Kennedy Adams · Accepted Answer

We first get all the denominators the same:

#3/4xx6/6<=x-7/8xx3/3<5/6xx4/4# #18/24<=x-21/24<20/24# We now add #21/24# to all three terms: #18/24+21/24<=x-cancel(21/24)+cancel(21/24)<20/24+21/24# #39/24<=x<41/24#

Jameson Allen · Answer

undefined To solve the inequality $\frac{3}{4} \leq x - \frac{7}{8} < \frac{5}{6}$, you need to isolate $x$ by performing operations to both sides of the inequality.

1. Start with the inequality:
$$\frac{3}{4} \leq x - \frac{7}{8} < \frac{5}{6}$$

2. Add $\frac{7}{8}$ to all parts of the inequality:
$$\frac{3}{4} + \frac{7}{8} \leq x - \frac{7}{8} + \frac{7}{8} < \frac{5}{6} + \frac{7}{8}$$

3. Simplify each part:
$$\frac{3}{4} + \frac{7}{8} \leq x < \frac{5}{6} + \frac{7}{8}$$
$$\frac{6}{8} + \frac{7}{8} \leq x < \frac{4}{6} + \frac{7}{8}$$
$$\frac{13}{8} \leq x < \frac{8}{8} + \frac{14}{12}$$
$$\frac{13}{8} \leq x < \frac{22}{12} + \frac{14}{12}$$
$$\frac{13}{8} \leq x < \frac{36}{12}$$

4. Simplify the fractions:
$$\frac{13}{8} \leq x < 3$$

Therefore, the solution to the inequality is $x$ such that $\frac{13}{8} \leq x < 3$.

How do you solve #\frac { 3} { 4} \leq x - \frac { 7} { 8} &lt; \frac { 5} { 6}#?

How do you solve #\frac { 3} { 4} \leq x - \frac { 7} { 8} < \frac { 5} { 6}#?