How do you solve #1

Question

How do you solve #1< 3x - 2\leq 10#?

Abigail Allen · Accepted Answer

See a solution process below:

First, add #color(red)(2)# to each segment of the system of inequalities to isolate the #x# term while keeping the system balanced: #1 + color(red)(2) < 3x - 2 + color(red)(2) <= 10 + color(red)(2)# #3 < 3x - 0 <= 12# #3 < 3x <= 12# Now, divide each segment by #color(red)(3)# to solve for #x# while keeping the system balanced: #3/color(red)(3) < (3x)/color(red)(3) <= 12/color(red)(3)# #1 < (color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) <= 4# #1 < x <= 4# Or #x > 1#; #x <= 4# Or, in interval notation: #(1, 4]#

Savannah Anderson · Answer

undefined To solve the inequality $1 < 3x - 2 \leq 10$, you would first add 2 to all parts of the inequality to isolate $3x$. Then, you divide each part by 3 to solve for $x$. The solution is $1 < x \leq 4$.

Genesis Allen · Answer

undefined To solve $1 < 3x - 2 \leq 10$, you first isolate the variable $x$ within the compound inequality.

Add 2 to all parts of the compound inequality:

$1 + 2 < 3x - 2 + 2 \leq 10 + 2$

This simplifies to:

$3 < 3x \leq 12$

Next, divide all parts by 3:

$\frac{3}{3} < \frac{3x}{3} \leq \frac{12}{3}$

This simplifies to:

$1 < x \leq 4$

Therefore, the solution to the inequality is $1 < x \leq 4$.

How do you solve #1&lt; 3x - 2\leq 10#?

How do you solve #1< 3x - 2\leq 10#?