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3 years ago

What is 8(c-9)=6(2c-12)-4c? Solve for c. Please show your work.

Mathematics

1 answer:

Dafna11 [192]3 years ago

4 0

Answer:

c= ℝ

Step-by-step explanation:

8(c-9)=6(2c-12)-4c

Distribute left side.

8*c+8*-9=6(2c-12)-4c

8c-72=6(2c-12)-4c

Distribte right side.

8c-72=6*2c+6*-12-4c

8c-72=12c-72-4c

Combine like terms.

8c-72=8c-72

Since the two sides are exactly the same, this means that any number for c will satisfy the equation.

Therefore, c= ℝ (all real numbers)

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Please check the explanation.

Step-by-step explanation:

Given the inequality

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substituting x = 4 in -6 < -2x

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Thus, x = 4 does not satisfiy the inequality -6 < -2x

∴ x = 4 is the NOT a solution to the inequality -6 < -2x.

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Part c) Find another value of x that is a solution to both inequalities.

solving -2x < 10

$-2x\:$

Multiply both sides by -1 (reverses the inequality)

$\left(-2x\right)\left(-1\right)>10\left(-1\right)$

Simplify

$2x>-10$

Divide both sides by 2

$\frac{2x}{2}>\frac{-10}{2}$

$x>-5$

$-2x-5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-5,\:\infty \:\right)\end{bmatrix}$

solving -6 < -2x

-6 < -2x

switch sides

$-2x>-6$

Multiply both sides by -1 (reverses the inequality)

$\left(-2x\right)\left(-1\right)$

Simplify

$2x$

Divide both sides by 2

$\frac{2x}{2}$

$x$

$-6$

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$\left(-\infty \:,\:3\right)$

$\left(-5,\:\infty \:\right)$

The intersection of these two intervals would be the solution to both inequalities.

$\left(-\infty \:,\:3\right)$ and $\left(-5,\:\infty \:\right)$

As x = 1 is included in both intervals.

so x = 1 would be another solution common to both inequalities.

<h3>SUBSTITUTING x = 1</h3>

FOR -2x < 10

substituting x = 1 in -2x < 10

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TRUE!

Thus, x = 1 satisfies the inequality -2x < 10.

∴ x = 1 is the solution to the inequality -2x < 10.

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substituting x = 1 in -6 < -2x

-6 < -2x

-6 < -2(1)

-6 < -2

TRUE!

Thus, x = 1 satisfies the inequality -6 < -2x

∴ x = 1 is the solution to the inequality -6 < -2x.

Conclusion:

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