Solved on Aug 30, 2023

Find $x$ given $AC=22$ , $BC=x+14$ , and $AB=x+10$ .

STEP 1

Assumptions1. The length of line segment AC is22 units. . The length of line segment BC is x +14 units.
3. The length of line segment AB is x +10 units.
4. The line segments form a straight line, so AC = AB + BC.

STEP 2

We can express the relationship between the line segments as an equation.
$AC = AB + BC$

STEP 3

Now, substitute the given values for AC, AB, and BC into the equation.
$22 = (x +10) + (x +14)$

STEP 4

implify the right side of the equation.
$22 =2x +24$

STEP 5

To isolate x, subtract24 from both sides of the equation.
$22 -24 =2x +24 -24$

STEP 6

implify both sides of the equation.
$-2 =2x$

STEP 7

Finally, divide both sides of the equation by2 to solve for x.
$x = -2 /2$

STEP 8

Calculate the value of x.
$x = -2 /2 = -1$ The value of x is -1.

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Find $x$ given $AC=22$ , $BC=x+14$ , and $AB=x+10$ .

STEP 1

Assumptions1. The length of line segment AC is22 units. . The length of line segment BC is x +14 units.
3. The length of line segment AB is x +10 units.
4. The line segments form a straight line, so AC = AB + BC.

STEP 2

We can express the relationship between the line segments as an equation.
$AC = AB + BC$

STEP 3

Now, substitute the given values for AC, AB, and BC into the equation.
$22 = (x +10) + (x +14)$

STEP 4

implify the right side of the equation.
$22 =2x +24$

STEP 5

To isolate x, subtract24 from both sides of the equation.
$22 -24 =2x +24 -24$

STEP 6

implify both sides of the equation.
$-2 =2x$

STEP 7

Finally, divide both sides of the equation by2 to solve for x.
$x = -2 /2$

STEP 8

Calculate the value of x.
$x = -2 /2 = -1$ The value of x is -1.

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Find xxx given AC=22AC=22AC=22, BC=x+14BC=x+14BC=x+14, and AB=x+10AB=x+10AB=x+10.

STEP 1

Assumptions1. The length of line segment AC is22 units. . The length of line segment BC is x +14 units.3. The length of line segment AB is x +10 units.4. The line segments form a straight line, so AC = AB + BC.

STEP 2

We can express the relationship between the line segments as an equation.AC=AB+BCAC = AB + BCAC=AB+BC

STEP 3

Now, substitute the given values for AC, AB, and BC into the equation.22=(x+10)+(x+14)22 = (x +10) + (x +14)22=(x+10)+(x+14)

STEP 4

implify the right side of the equation.22=2x+2422 =2x +2422=2x+24

STEP 5

To isolate x, subtract24 from both sides of the equation.22−24=2x+24−2422 -24 =2x +24 -2422−24=2x+24−24

STEP 6

implify both sides of the equation.−2=2x-2 =2x−2=2x

STEP 7

Finally, divide both sides of the equation by2 to solve for x.x=−2/2x = -2 /2x=−2/2

STEP 8

Calculate the value of x.x=−2/2=−1x = -2 /2 = -1x=−2/2=−1The value of x is -1.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find $x$ given $AC=22$ , $BC=x+14$ , and $AB=x+10$ .

Assumptions1. The length of line segment AC is22 units. . The length of line segment BC is x +14 units.
3. The length of line segment AB is x +10 units.
4. The line segments form a straight line, so AC = AB + BC.

We can express the relationship between the line segments as an equation.
$AC = AB + BC$

Now, substitute the given values for AC, AB, and BC into the equation.
$22 = (x +10) + (x +14)$

implify the right side of the equation.
$22 =2x +24$

To isolate x, subtract24 from both sides of the equation.
$22 -24 =2x +24 -24$

implify both sides of the equation.
$-2 =2x$

Finally, divide both sides of the equation by2 to solve for x.
$x = -2 /2$

Calculate the value of x.
$x = -2 /2 = -1$ The value of x is -1.