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.

William Cleghorn
2021-12-20
Answered

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.

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.

You can still ask an expert for help

Janet Young

Answered 2021-12-21
Author has **32** answers

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.

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,

On solving algebraically,

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,

On solving algebraically,

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,

Hence, the value of the unknown number is less than or equal to 2.

Janet Young

Answered 2021-12-22
Author has **32** answers

Answer:

1.$x=\frac{1}{7}$

2.$x=10$

Step-by-step explanation:

1.$3x+7=8-4x$

$3x+7=8\pm 4x$

$3x+7=-4x+8$

$3x+7+4x=-4x+8+4x$

$7x+7=8$

$7x+7-7=8-7$

$7x=1$

$7\frac{x}{7}=\frac{1}{7}$

$x=\frac{1}{7}$

2.$9x-12=8x-2$

$9x-12-8x=8x-2-8x$

$x-12=-2$

$x-12+12=-2+12$

$x=10$

1.

2.

Step-by-step explanation:

1.

2.

Don Sumner

Answered 2021-12-28
Author has **35** answers

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.

Hence, the value of the unknown number is less than or equal to 2.

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