Translate each statement into a linear equality or inequalit

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.
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Expert Answer

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=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.
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Janet Young
Answered 2021-12-22 Author has 32 answers
Answer:
1. x=17
2. x=10
Step-by-step explanation:
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
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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.
52x73x
3x2x75
x2
Hence, the value of the unknown number is less than or equal to 2.

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