Math / Algebra

Question1. Solve the following equations for $x$ . a. $3 x-5=16$

Studdy Solution

STEP 1

1. The equation $3x - 5 = 16$ is a linear equation in one variable.
2. The goal is to solve for $x$ by isolating it on one side of the equation.
3. Basic algebraic operations such as addition and division will be used.

STEP 2

1. Isolate the term containing $x$ by eliminating the constant term on the same side.
2. Solve for $x$ by performing the necessary algebraic operation.
3. Verify the solution by substituting it back into the original equation.

STEP 3

To isolate the term containing $x$ , add 5 to both sides of the equation:
$3x - 5 + 5 = 16 + 5$
Simplify the equation:
$3x = 21$

STEP 4

Now, solve for $x$ by dividing both sides of the equation by 3:
$\frac{3x}{3} = \frac{21}{3}$
Simplify the equation:
$x = 7$

STEP 5

Verify the solution by substituting $x = 7$ back into the original equation:
$3(7) - 5 = 16$
Calculate the left-hand side:
$21 - 5 = 16$
Since both sides of the equation are equal, the solution is verified.
The solution is:
$\boxed{7}$

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Question1. Solve the following equations for $x$ . a. $3 x-5=16$

Studdy Solution

STEP 1

1. The equation $3x - 5 = 16$ is a linear equation in one variable.
2. The goal is to solve for $x$ by isolating it on one side of the equation.
3. Basic algebraic operations such as addition and division will be used.

STEP 2

1. Isolate the term containing $x$ by eliminating the constant term on the same side.
2. Solve for $x$ by performing the necessary algebraic operation.
3. Verify the solution by substituting it back into the original equation.

STEP 3

To isolate the term containing $x$ , add 5 to both sides of the equation:
$3x - 5 + 5 = 16 + 5$
Simplify the equation:
$3x = 21$

STEP 4

Now, solve for $x$ by dividing both sides of the equation by 3:
$\frac{3x}{3} = \frac{21}{3}$
Simplify the equation:
$x = 7$

STEP 5

Verify the solution by substituting $x = 7$ back into the original equation:
$3(7) - 5 = 16$
Calculate the left-hand side:
$21 - 5 = 16$
Since both sides of the equation are equal, the solution is verified.
The solution is:
$\boxed{7}$

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Question1. Solve the following equations for xxx. a. 3x−5=163 x-5=163x−5=16

Studdy Solution

STEP 1

1. The equation 3x−5=16 3x - 5 = 16 3x−5=16 is a linear equation in one variable.2. The goal is to solve for x x x by isolating it on one side of the equation.3. Basic algebraic operations such as addition and division will be used.

STEP 2

1. Isolate the term containing x x x by eliminating the constant term on the same side.2. Solve for x x x by performing the necessary algebraic operation.3. Verify the solution by substituting it back into the original equation.

STEP 3

To isolate the term containing x x x, add 5 to both sides of the equation:3x−5+5=16+5 3x - 5 + 5 = 16 + 5 3x−5+5=16+5Simplify the equation:3x=21 3x = 21 3x=21

STEP 4

Now, solve for x x x by dividing both sides of the equation by 3:3x3=213 \frac{3x}{3} = \frac{21}{3} 33x​=321​Simplify the equation:x=7 x = 7 x=7

STEP 5

Verify the solution by substituting x=7 x = 7 x=7 back into the original equation:3(7)−5=16 3(7) - 5 = 16 3(7)−5=16Calculate the left-hand side:21−5=16 21 - 5 = 16 21−5=16Since both sides of the equation are equal, the solution is verified. The solution is:7 \boxed{7} 7​

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Studdy solves anything!

Start learning now

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

Question1. Solve the following equations for $x$ . a. $3 x-5=16$

1. The equation $3x - 5 = 16$ is a linear equation in one variable.
2. The goal is to solve for $x$ by isolating it on one side of the equation.
3. Basic algebraic operations such as addition and division will be used.

1. Isolate the term containing $x$ by eliminating the constant term on the same side.
2. Solve for $x$ by performing the necessary algebraic operation.
3. Verify the solution by substituting it back into the original equation.

To isolate the term containing $x$ , add 5 to both sides of the equation:
$3x - 5 + 5 = 16 + 5$
Simplify the equation:
$3x = 21$

Now, solve for $x$ by dividing both sides of the equation by 3:
$\frac{3x}{3} = \frac{21}{3}$
Simplify the equation:
$x = 7$

Verify the solution by substituting $x = 7$ back into the original equation:
$3(7) - 5 = 16$
Calculate the left-hand side:
$21 - 5 = 16$
Since both sides of the equation are equal, the solution is verified.
The solution is:
$\boxed{7}$