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Elena-2011 [213]
2 years ago
9

The solution set for the inequality x + 4 ≤ 1/2 (x - 3) includes -11 as an element.

Mathematics
1 answer:
Sindrei [870]2 years ago
6 0

Answer:

<h2>x ≤ -11, Yes. The solution set include -11.</h2>

Step-by-step explanation:

x+4\leq\dfrac{1}{2}(x-3)\qquad\text{multiply both sides by 2}\\\\2x+8\leq1(x-3)\\\\2x+8\leq x-3\qquad\text{subtract 8 from both sides}\\\\2x\leq x-11\qquad\text{subtract x from both sides}\\\\\boxed{x\leq-11}

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How do you solve (7x + 5) - (3x + 2)
Korolek [52]

Answer:

x = 0.75

Step-by-step explanation:

Simplifying

(7x + -5) + -1(3x + -2) = 0

Reorder the terms:

(-5 + 7x) + -1(3x + -2) = 0

Remove parenthesis around (-5 + 7x)

-5 + 7x + -1(3x + -2) = 0

Reorder the terms:

-5 + 7x + -1(-2 + 3x) = 0

-5 + 7x + (-2 * -1 + 3x * -1) = 0

-5 + 7x + (2 + -3x) = 0

Reorder the terms:

-5 + 2 + 7x + -3x = 0

Combine like terms: -5 + 2 = -3

-3 + 7x + -3x = 0

Combine like terms: 7x + -3x = 4x

-3 + 4x = 0

Solving

-3 + 4x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.

-3 + 3 + 4x = 0 + 3

Combine like terms: -3 + 3 = 0

0 + 4x = 0 + 3

4x = 0 + 3

Combine like terms: 0 + 3 = 3

4x = 3

Divide each side by '4'.

x = 0.75

Simplifying

x = 0.75

6 0
2 years ago
Read 2 more answers
Carlos used 6 boards to build 2/3 of a front porch. How many boards will Carlos use to build the whole porch? Express your answe
antiseptic1488 [7]

Answer:

9 boards

Step-by-step explanation:

2/3 of the porch= 6 boards

so to figure out how much one third of the porch needs you find half of what it takes to fill in 2/3 of the porch and you get 3.

so 3=1/3 of the porch

then you simply do 3times 3 or 3+3+3 and you get 9

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8 0
3 years ago
8. Solve the following proportion (1 point)
Arturiano [62]

Answer:

97.5

Step-by-step explanation:

Cross multiply

2 * x = 2x

15 * 13 = 195

2x = 195

2x/2 = 195/2

x = 97.5

[RevyBreeze]

6 0
2 years ago
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Any one good at factoring?
svetlana [45]
The student went wrong in step three.  the solutions should have been -3 and 5
8 0
3 years ago
Factorize x^4 + 2x^3 - 11x^2 - 12x + 36 <br><br>I need the steps.<br>Please i need this for today.
Yuliya22 [10]

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6 0
2 years ago
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