50 POINTS AND BRAINLIEST IF CAN SOLVE WITH CORRECT ANSWER AND PROVIDE STEPS

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ira [324]

<h2>Solving Equations</h2>

To solve linear equations, we must perform inverse operations on both sides of the equal sign to <em>cancel values out</em>.

If something is being added to x, subtract it from both sides.
If something is being subtracted from x, add it on both sides.
Same with multiplication and division. If x is being divided, multiply. If x is being multiplied, divide.

We perform inverse operations to<em> combine like terms</em>. This means to get x to one side and everything else on the other.

<h2>Solving the Questions</h2><h3>Question 1</h3>

$5x+7=15$

Because 7 is being added to x, subtract it from both sides:

$5x+7-7=15-7\\5x=8$

Because x is being multiplied by 5, divide both sides by 5:

$\dfrac{5x}{5}=\dfrac{8}{5}\\\\x=\dfrac{8}{5}$

Therefore. $x=\dfrac{8}{5}$ .

<h3>Question 2</h3>

$7x+4=5x-18$

Here, we can group all the x values on the left side of the equation. Subtract 5x from both sides:

$7x+4-5x=5x-18-5x\\2x+4=-18$

To isolate x, subtract 4 from both sides:

$2x+4-4=-18-4\\2x=-22$

Divide both sides by 2:

$\dfrac{2x}{2}=\dfrac{-22}{2}\\\\x=-11$

Therefore, $x=-11$ .

6 0

1 year ago

Answer the photo below thanks!!<br> —Explain your answer please—

UkoKoshka [18]

(17X22)+((12X19)/2)=488cm^2

8 0

2 years ago

What three consecutive integers equal -87?

olchik [2.2K]

Answer:

What three consecutive integers have a sum of 87? Which means that the first number is 28, the second number is 28 + 1 and the third number is 28 + 2. Therefore, three consecutive integers that add up to 87 are 28, 29, and 30. We know our answer is correct because 28 + 29 + 30 equals 87 as displayed above.

Step-by-step explanation:

Consecutive integers are as simple as 1, 2, 3!

Integers are consecutive if one follows another. How do we "jump" from one integer to the next? We add 1, right? 7, 8 and 9 are three consecutive integers. Add one to 7 to get 8 and add one more to get 9.

Now lets think about this in algebraic terms. Lets name these consecutive integers , x, y and z.

The problem tells us that their sum is -87. (Recall, "sum" is just a fancy word for the answer when we add.)

x+y+z = -87

Here is the trick! We need to rewrite this equation so that we have only one variable. Easy!

y is one more that x, so y= x+1

And z is one more than y, so z= y+1. But y is also equal to (x+1)! So z=y+1=(x+1)+1=x+2

Now we have a problem that we can solve! x+(x+1)+(x+2)=-87.

Combining term.: 3x+3=-87

Subtract 3 from both sides of the equation: 3x=84

Divide each side of the equation by 3: x=28

We have solved for x, but we are not done! We need to find y and z. I know you can do this. Remember y is one more than x and z is one more than y.

Check your work! Make sure these three consecutive numbers do in fact add up to -87.

4 0

2 years ago

21. How many different integers can have the same absolute<br> value?<br> Give an example.

charle [14.2K]

2 integers at a time!

6 0

3 years ago

A portrait has dimensions of 30“ x 60“ and is surrounded by a frame of uniform width. If the total area (Portrait plus frame) is

Law Incorporation [45]

Answer:

The width of the is 4 inches

Step-by-step explanation:

Assume that the width of the frame is x

∵ The width of the fame is x inches

→ That means each dimension will increase by 2x ⇒ x from each side

∵ The portrait has dimensions of 30“ x 60“

∴ Its dimensions including the frame = (30 + 2x) × (60 + 2x)

∴ The total area of the portrait plus frame = (30 + 2x)(60 + 2x)

→ Multiply the brackets

∵ (30 + 2x)(60 + 2x) = 30(60) + 30(2x) + 2x(60) + (2x)(2x)

∴ (30 + 2x)(60 + 2x) = 1800 + 60x + 120x + 4x²

→ Add the like terms

∴ (30 + 2x)(60 + 2x) = 1800 + 180x + 4x²

∴ The total area of the portrait plus frame = 4x² + 180x + 1800

∵ The total area of the portrait plus frame = 2584 square inches

→ Equate the two right sides of the area

∴ 4x² + 180x + 1800 = 2584

→ Subtract 2584 from both sides

∴ 4x² + 180x + 1800 - 2584 = 0

→ Add the like terms in the left side

∴ 4x² + 180x - 784 = 0

→ Divide all terms by 4 to simplify

∴ x² + 45x - 196 = 0

→ Factorize it to find the value of x

∵ x² + 45x - 196 = (x - 4)(x + 49)

→ Equate the right side by 0

∴ (x - 4)(x + 49) = 0

→ Equate each factor by 0

∵ x - 4 = 0

→ Add 4 to both sides to find x

∴ x = 4

∵ x + 49 = 0

→ Subtract 49 from both sides to find x

∴ x = -49 ⇒ refused it x can not be -ve (no negative dimensions)

∴ The width of the is 4 inches

7 0

2 years ago