Translate each statement into a linear equality or inequalit

William Cleghorn

William Cleghorn

Answered question

2021-12-20

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.

Answer & Explanation

Janet Young

Janet Young

Beginner2021-12-21Added 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=4x8
On solving algebraically,
7+3x=4x8
4x3x=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,
129x=28x
On solving algebraically,
129x=28
9x8x=122
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,
52x73x
3x2x75
x2
Hence, the value of the unknown number is less than or equal to 2.
Janet Young

Janet Young

Beginner2021-12-22Added 32 answers

Results : 
1. x=17 
2. x=10 
Solution :
1. 3x+7=84x 
3x+7=8±4x 
3x+7=4x+8 
3x+7+4x=4x+8+4x 
7x+7=8 
7x+77=87 
7x=1 
7x7=17 
x=17 
2. 9x12=8x2 
9x128x=8x28x 
x12=2 
x12+12=2+12 
x=10

Don Sumner

Don Sumner

Skilled2021-12-28Added 184 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
Answer: 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
Therefore, 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.
52x73x
3x2x75
x2
Answer: The value of the unknown number is less than or equal to 2.

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