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3 years ago

Given the function f(x) = –5|x + 1| + 3, for what values of x is f(x) = –12?

Mathematics

1 answer:

Sonbull [250]3 years ago

6 0

The correct answer is x = 2 and x = -4.

In order to solve for this, you first need to plug in the f(x) value and solve for the absolute value statement.

f(x) = -5|x + 1| + 3

-12 = -5|x + 1| + 3 ---> subtract 3 from both sides.

-15 = -5|x + 1|----> divide both sides by -5.

3 = |x + 1|

Now that we have solved for the absolute value portion, we need to solve this equation twice. Once removing the absolute value and solving and the other by removing it and making the 3 negative. This is because even if the inside of the markers was -3, it would give us a 3 answer.

3 = x + 1

2 = x

Then the negative version.

-3 = x + 1

-4 = x

And there are your two answers.

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Drag the tiles to the boxes to form correct pairs. Match the pairs of equivalent expressions.

Rashid [163]

Answer:

The following pairs/results are matched:

$5\left(2t+1\right)+\left(-7t+28\right)$ = $3t+33$
$3\left(3t-4\right)-\left(2t+10\right)$ = $7t-22$

$\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$ = $\frac{16t}{3}-\frac{23}{5}$

$\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$ = $-\frac{11}{4}t+36$

Step-by-step explanation:

Lets solve all the expressions to match the results.

$5\left(2t+1\right)+\left(-7t+28\right)$

Solving the expression

$5\left(2t+1\right)+\left(-7t+28\right)$

$\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a$

$5\left(2t+1\right)-7t+28$

$10t+5-7t+28$

$3t+33$

Therefore, $5\left(2t+1\right)+\left(-7t+28\right)$ = $3t+33$

$3\left(3t-4\right)-\left(2t+10\right)$

Solving the expression

$3\left(3t-4\right)-\left(2t+10\right)$

$9t-12-\left(2t+10\right)$

$9t-12-2t-10$

$7t-22$

Therefore, $3\left(3t-4\right)-\left(2t+10\right)$ = $7t-22$

$\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$

Solving the expression

$\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$4t-\frac{8}{5}-\left(3-\frac{4}{3}t\right)$

$4t-\frac{8}{5}-\left(-\frac{4t}{3}+3\right)$

$4t-\frac{8}{5}-3+\frac{4t}{3}$

$-3-\frac{8}{5}:\quad -\frac{23}{5}$ and $\frac{4t}{3}+4t:\quad \frac{16t}{3}$

So,

$4t-\frac{8}{5}-3+\frac{4t}{3}$ will become $\frac{16t}{3}-\frac{23}{5}$

Therefore, $\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$ = $\frac{16t}{3}-\frac{23}{5}$

$\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$

Solving the expression

$\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$-\frac{9}{2}t+3+\frac{7}{4}t+33$

$\mathrm{Group\:like\:terms}$

$\frac{9}{2}t+\frac{7}{4}t+3+33$

$\mathrm{Add\:similar\:elements:}\:-\frac{9}{2}t+\frac{7}{4}t=-\frac{11}{4}t$

$-\frac{11}{4}t+3+33$

$-\frac{11}{4}t+36$

Therefore, $\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$ = $-\frac{11}{4}t+36$

Thus, the following pairs/results are matched:

$5\left(2t+1\right)+\left(-7t+28\right)$ = $3t+33$
$3\left(3t-4\right)-\left(2t+10\right)$ = $7t-22$

$\left(4t-\frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)$ = $\frac{16t}{3}-\frac{23}{5}$

$\left(-\frac{9}{2}t+3\right)+\left(\frac{7}{4}t+33\right)$ = $-\frac{11}{4}t+36$

Keywords: algebraic expression

Learn more about algebraic expression from brainly.com/question/11336599

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3 years ago

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What is the x-coordinate of the solution to the following system of equations?

tatyana61 [14]

Answer

X-2y = 2

3x + y = 6

Ox=-2

Ox=0

Ox=2

Ox=3

= 0

Step-by-step explanation:

easy

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3 years ago

Ali has x cards.

valentina_108 [34]

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━

If Ali has x cards, then Belinda has 2x cards.

If Ali has x cards, then Charlie has x+5 cards.

2x (Belinda) + x+5 (Charlie) + x (Ali) = 33 (total)

2x + x+5 + x = 33

Now simplify the equation... x+x+5 can be simplified as 2x+5.

2x+5 plus 2x can become 4x+5.

So their total number is 4x+5.

So 4x+5=33.

You want to isolate the variables and numbers.

To remove the 5 from the left side, subtract 5 from both sides.

4x+5-5=4x - 33-5=28

So the equation now is 4x=28

To remove the 4, divide each side by 4.

4x÷4=x - 28÷4=7

So x equals 7, Ali has 7 cards.

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3 years ago

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Nine times the sum of n and one

Sveta_85 [38]

Answer:

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3 years ago

What is the value of 10P10

storchak [24]

ONO THAT NOT THE ANSWER THIS IS [3,628,800] 10P10=10, AND 0!= 10 TIMES 9 TIMES 8 TIMES 7 TIMES 6 TIMES 5 TIMES 4 TIMES 3 TIMES 2 TIMES 1= 3,628,800.

7 0

3 years ago