Translate each statement into a linear equality or inequalit

Step 1
Given:
The objective is to solve the given statements algebraically.
Step 2
1) It is given that, seven more than three times a number equals eight less than four times the number.
Consider the unknown number as x. Then the equation can be represented as,
${\displaystyle 7+3x=4x-8}$
On solving algebraically,
${\displaystyle 7+3x=4x-8}$
${\displaystyle 4x-3x=8+7}$
${\displaystyle x=15}$
Hence, the value of the unknown number is 15.
Step 3
2) It is given that twelve minus nine times a number is the same as two minus eight times a number.
Consider the unknown number as x. Then the equation can be represented as,
${\displaystyle 12-9x=2-8x}$
On solving algebraically,
${\displaystyle 12-9x=2-8}$
${\displaystyle 9x-8x=12-2}$
${\displaystyle x=10}$
Hence, the value of the unknown number is 10.
Step 4
3) It is given that five minus two times x is less than or equal to seven minus three times x.
The given equation can be represented as,
${\displaystyle 5-2x\le 7-3x}$
${\displaystyle 3x-2x\le 7-5}$
${\displaystyle x\le 2}$
Hence, the value of the unknown number is less than or equal to 2.