Solved on Jan 18, 2024

Find the value of $x$ that satisfies the equation $(1+7)(4+1x) = 15 - 2.5(x+1)$ , rounded to two decimal places.

STEP 1

Assumptions
1. We need to solve the equation for $x$ .
2. The equation is given as $(1+7)(4+1x)=15-2.5(x+1)$ .
3. The solution for $x$ should be rounded to two decimal places.

STEP 2

First, simplify the left-hand side of the equation by performing the addition inside the parentheses.
$(1+7)(4+x) = 15-2.5(x+1)$

STEP 3

Now, simplify the addition.
$8(4+x) = 15-2.5(x+1)$

STEP 4

Next, distribute the 8 on the left-hand side.
$8 \cdot 4 + 8 \cdot x = 15 - 2.5(x+1)$

STEP 5

Perform the multiplication.
$32 + 8x = 15 - 2.5(x+1)$

STEP 6

Now, distribute the $-2.5$ on the right-hand side.
$32 + 8x = 15 - 2.5x - 2.5$

STEP 7

Combine like terms on the right-hand side.
$32 + 8x = 12.5 - 2.5x$

STEP 8

To isolate $x$ , move all terms containing $x$ to one side and the constant terms to the other side. Start by adding $2.5x$ to both sides.
$32 + 8x + 2.5x = 12.5 - 2.5x + 2.5x$

STEP 9

Combine like terms.
$32 + 10.5x = 12.5$

STEP 10

Now, subtract $32$ from both sides to isolate the term with $x$ .
$32 + 10.5x - 32 = 12.5 - 32$

STEP 11

Simplify both sides.
$10.5x = -19.5$

STEP 12

Finally, divide both sides by $10.5$ to solve for $x$ .
$\frac{10.5x}{10.5} = \frac{-19.5}{10.5}$

STEP 13

Perform the division to find the value of $x$ .
$x = \frac{-19.5}{10.5}$

STEP 14

Calculate the value of $x$ .
$x = -\frac{19.5}{10.5}$

STEP 15

Simplify the fraction.
$x = -\frac{39}{21}$

STEP 16

Reduce the fraction to lowest terms.
$x = -\frac{13}{7}$

STEP 17

Convert the fraction to a decimal.
$x = -1.857142857...$

STEP 18

Round the solution to two decimal places.
$x \approx -1.86$
The solution to the equation is $x \approx -1.86$ .

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Find the value of $x$ that satisfies the equation $(1+7)(4+1x) = 15 - 2.5(x+1)$ , rounded to two decimal places.

STEP 1

Assumptions
1. We need to solve the equation for $x$ .
2. The equation is given as $(1+7)(4+1x)=15-2.5(x+1)$ .
3. The solution for $x$ should be rounded to two decimal places.

STEP 2

First, simplify the left-hand side of the equation by performing the addition inside the parentheses.
$(1+7)(4+x) = 15-2.5(x+1)$

STEP 3

Now, simplify the addition.
$8(4+x) = 15-2.5(x+1)$

STEP 4

Next, distribute the 8 on the left-hand side.
$8 \cdot 4 + 8 \cdot x = 15 - 2.5(x+1)$

STEP 5

Perform the multiplication.
$32 + 8x = 15 - 2.5(x+1)$

STEP 6

Now, distribute the $-2.5$ on the right-hand side.
$32 + 8x = 15 - 2.5x - 2.5$

STEP 7

Combine like terms on the right-hand side.
$32 + 8x = 12.5 - 2.5x$

STEP 8

To isolate $x$ , move all terms containing $x$ to one side and the constant terms to the other side. Start by adding $2.5x$ to both sides.
$32 + 8x + 2.5x = 12.5 - 2.5x + 2.5x$

STEP 9

Combine like terms.
$32 + 10.5x = 12.5$

STEP 10

Now, subtract $32$ from both sides to isolate the term with $x$ .
$32 + 10.5x - 32 = 12.5 - 32$

STEP 11

Simplify both sides.
$10.5x = -19.5$

STEP 12

Finally, divide both sides by $10.5$ to solve for $x$ .
$\frac{10.5x}{10.5} = \frac{-19.5}{10.5}$

STEP 13

Perform the division to find the value of $x$ .
$x = \frac{-19.5}{10.5}$

STEP 14

Calculate the value of $x$ .
$x = -\frac{19.5}{10.5}$

STEP 15

Simplify the fraction.
$x = -\frac{39}{21}$

STEP 16

Reduce the fraction to lowest terms.
$x = -\frac{13}{7}$

STEP 17

Convert the fraction to a decimal.
$x = -1.857142857...$

STEP 18

Round the solution to two decimal places.
$x \approx -1.86$
The solution to the equation is $x \approx -1.86$ .

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Find the value of xxx that satisfies the equation (1+7)(4+1x)=15−2.5(x+1)(1+7)(4+1x) = 15 - 2.5(x+1)(1+7)(4+1x)=15−2.5(x+1), rounded to two decimal places.

STEP 1

Assumptions1. We need to solve the equation for xxx.2. The equation is given as (1+7)(4+1x)=15−2.5(x+1)(1+7)(4+1x)=15-2.5(x+1)(1+7)(4+1x)=15−2.5(x+1).3. The solution for xxx should be rounded to two decimal places.

STEP 2

First, simplify the left-hand side of the equation by performing the addition inside the parentheses.(1+7)(4+x)=15−2.5(x+1)(1+7)(4+x) = 15-2.5(x+1)(1+7)(4+x)=15−2.5(x+1)

STEP 3

Now, simplify the addition.8(4+x)=15−2.5(x+1)8(4+x) = 15-2.5(x+1)8(4+x)=15−2.5(x+1)

STEP 4

Next, distribute the 8 on the left-hand side.8⋅4+8⋅x=15−2.5(x+1)8 \cdot 4 + 8 \cdot x = 15 - 2.5(x+1)8⋅4+8⋅x=15−2.5(x+1)

STEP 5

Perform the multiplication.32+8x=15−2.5(x+1)32 + 8x = 15 - 2.5(x+1)32+8x=15−2.5(x+1)

STEP 6

Now, distribute the −2.5-2.5−2.5 on the right-hand side.32+8x=15−2.5x−2.532 + 8x = 15 - 2.5x - 2.532+8x=15−2.5x−2.5

STEP 7

Combine like terms on the right-hand side.32+8x=12.5−2.5x32 + 8x = 12.5 - 2.5x32+8x=12.5−2.5x

STEP 8

To isolate xxx, move all terms containing xxx to one side and the constant terms to the other side. Start by adding 2.5x2.5x2.5x to both sides.32+8x+2.5x=12.5−2.5x+2.5x32 + 8x + 2.5x = 12.5 - 2.5x + 2.5x32+8x+2.5x=12.5−2.5x+2.5x

STEP 9

Combine like terms.32+10.5x=12.532 + 10.5x = 12.532+10.5x=12.5

STEP 10

Now, subtract 323232 from both sides to isolate the term with xxx.32+10.5x−32=12.5−3232 + 10.5x - 32 = 12.5 - 3232+10.5x−32=12.5−32

STEP 11

Simplify both sides.10.5x=−19.510.5x = -19.510.5x=−19.5

STEP 12

Finally, divide both sides by 10.510.510.5 to solve for xxx.10.5x10.5=−19.510.5\frac{10.5x}{10.5} = \frac{-19.5}{10.5}10.510.5x​=10.5−19.5​

STEP 13

Perform the division to find the value of xxx.x=−19.510.5x = \frac{-19.5}{10.5}x=10.5−19.5​

STEP 14

Calculate the value of xxx.x=−19.510.5x = -\frac{19.5}{10.5}x=−10.519.5​

STEP 15

Simplify the fraction.x=−3921x = -\frac{39}{21}x=−2139​

STEP 16

Reduce the fraction to lowest terms.x=−137x = -\frac{13}{7}x=−713​

STEP 17

Convert the fraction to a decimal.x=−1.857142857...x = -1.857142857...x=−1.857142857...

STEP 18

Round the solution to two decimal places.x≈−1.86x \approx -1.86x≈−1.86The solution to the equation is x≈−1.86x \approx -1.86x≈−1.86.

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Find the value of $x$ that satisfies the equation $(1+7)(4+1x) = 15 - 2.5(x+1)$ , rounded to two decimal places.

Assumptions
1. We need to solve the equation for $x$ .
2. The equation is given as $(1+7)(4+1x)=15-2.5(x+1)$ .
3. The solution for $x$ should be rounded to two decimal places.

First, simplify the left-hand side of the equation by performing the addition inside the parentheses.
$(1+7)(4+x) = 15-2.5(x+1)$

Now, simplify the addition.
$8(4+x) = 15-2.5(x+1)$

Next, distribute the 8 on the left-hand side.
$8 \cdot 4 + 8 \cdot x = 15 - 2.5(x+1)$

Perform the multiplication.
$32 + 8x = 15 - 2.5(x+1)$

Now, distribute the $-2.5$ on the right-hand side.
$32 + 8x = 15 - 2.5x - 2.5$

Combine like terms on the right-hand side.
$32 + 8x = 12.5 - 2.5x$

To isolate $x$ , move all terms containing $x$ to one side and the constant terms to the other side. Start by adding $2.5x$ to both sides.
$32 + 8x + 2.5x = 12.5 - 2.5x + 2.5x$

Combine like terms.
$32 + 10.5x = 12.5$

Now, subtract $32$ from both sides to isolate the term with $x$ .
$32 + 10.5x - 32 = 12.5 - 32$

Simplify both sides.
$10.5x = -19.5$

Finally, divide both sides by $10.5$ to solve for $x$ .
$\frac{10.5x}{10.5} = \frac{-19.5}{10.5}$

Perform the division to find the value of $x$ .
$x = \frac{-19.5}{10.5}$

Calculate the value of $x$ .
$x = -\frac{19.5}{10.5}$

Simplify the fraction.
$x = -\frac{39}{21}$

Reduce the fraction to lowest terms.
$x = -\frac{13}{7}$

Convert the fraction to a decimal.
$x = -1.857142857...$

Round the solution to two decimal places.
$x \approx -1.86$
The solution to the equation is $x \approx -1.86$ .