# Translate each statement into a linear equality or inequalit

Translate each statement into a linear equality or inequality then solve algebraically.
1. Seven more than three times a number equals eight less than four times the number.
2. Twelve minus nine times a number is the same as two minus eight times the number.
3. Five minus two times x is less than or equal to seven minus three times x.
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Janet Young
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,
$7+3x=4x-8$
On solving algebraically,
$7+3x=4x-8$
$4x-3x=8+7$
$x=15$
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,
$12-9x=2-8x$
On solving algebraically,
$12-9x=2-8$
$9x-8x=12-2$
$x=10$
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,
$5-2x\le 7-3x$
$3x-2x\le 7-5$
$x\le 2$
Hence, the value of the unknown number is less than or equal to 2.
###### Not exactly what you’re looking for?
Janet Young
1. $x=\frac{1}{7}$
2. $x=10$
Step-by-step explanation:
1. $3x+7=8-4x$
$3x+7=8±4x$
$3x+7=-4x+8$
$3x+7+4x=-4x+8+4x$
$7x+7=8$
$7x+7-7=8-7$
$7x=1$
$7\frac{x}{7}=\frac{1}{7}$
$x=\frac{1}{7}$
2. $9x-12=8x-2$
$9x-12-8x=8x-2-8x$
$x-12=-2$
$x-12+12=-2+12$
$x=10$
###### Not exactly what you’re looking for?
Don Sumner

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,
7+3x=4x-8
7+3x=4x-8
4x-3x=8+7
x=15
Hence, the value of the unknown number is 15.
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,
12-9x=2-8x
12-9x=2-8
9x-8x=12-2
x=10
Hence, the value of the unknown number is 10.
3) It is given that five minus two times x is less than or equal to seven minus three times x.
$5-2x\le 7-3x$
$3x-2x\le 7-5$
$x\le 2$
Hence, the value of the unknown number is less than or equal to 2.