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Solve for U.

6u - 13u - 18 = -81
Simplify your answer as much as possible.

11 answers

To solve the equation \( 6u - 13u - 18 = -81 \), we first combine the like terms on the left side.

  1. Combine \( 6u \) and \( -13u \): \[ 6u - 13u = -7u \] So, the equation becomes: \[ -7u - 18 = -81 \]

  2. Next, we can isolate the term involving \( u \) by adding 18 to both sides of the equation: \[ -7u - 18 + 18 = -81 + 18 \] Simplifying both sides gives: \[ -7u = -63 \]

  3. Now, divide both sides by \(-7\) to solve for \( u \): \[ u = \frac{-63}{-7} \] Simplifying that gives: \[ u = 9 \]

Thus, the solution is: \[ \boxed{9} \]

Rewrite the equation below so that it does not have fractions.
3/4x - 3 = 7/10
Do not use decimals in your answer.

To rewrite the equation \(\frac{3}{4}x - 3 = \frac{7}{10}\) without fractions, we can eliminate the fractions by finding a common denominator.

The denominators present are 4 and 10. The least common multiple (LCM) of 4 and 10 is 20.

  1. Multiply every term in the equation by 20 to eliminate the fractions:

\[ 20 \left(\frac{3}{4}x\right) - 20 \cdot 3 = 20 \left(\frac{7}{10}\right) \]

  1. Now perform the multiplication:

    • For \(20 \left(\frac{3}{4}x\right)\): \[ 20 \times \frac{3}{4} = 5 \times 3 = 15x \]
    • For \(-20 \cdot 3\): \[ -20 \times 3 = -60 \]
    • For \(20 \left(\frac{7}{10}\right)\): \[ 20 \times \frac{7}{10} = 2 \times 7 = 14 \]

  2. Putting it all together, the equation becomes: \[ 15x - 60 = 14 \]

Thus, the rewritten equation without fractions is: \[ \boxed{15x - 60 = 14} \]

solve for x
z = 5x - 11y

To solve the equation \( z = 5x - 11y \) for \( x \), we can follow these steps:

  1. Start with the original equation: \[ z = 5x - 11y \]

  2. Add \( 11y \) to both sides to isolate the term with \( x \): \[ z + 11y = 5x \]

  3. Now, divide both sides by 5 to solve for \( x \): \[ x = \frac{z + 11y}{5} \]

Thus, the solution for \( x \) is: \[ \boxed{x = \frac{z + 11y}{5}} \]

what is the solution for 17 < 2v + 9
_

To solve the inequality \( 17 < 2v + 9 \), follow these steps:

  1. Subtract 9 from both sides to begin isolating the term with \( v \): \[ 17 - 9 < 2v \] This simplifies to: \[ 8 < 2v \]

  2. Divide both sides by 2 to solve for \( v \): \[ \frac{8}{2} < v \] This simplifies to: \[ 4 < v \]

  3. We can also write this as: \[ v > 4 \]

Thus, the solution to the inequality \( 17 < 2v + 9 \) is: \[ \boxed{v > 4} \]

x/3 - 15 greaterequal sign 13

To solve the inequality

\[ \frac{x}{3} - 15 \geq 13 \]

follow these steps:

  1. Add 15 to both sides to isolate the term with \( x \):

\[ \frac{x}{3} - 15 + 15 \geq 13 + 15 \]

This simplifies to:

\[ \frac{x}{3} \geq 28 \]

  1. Multiply both sides by 3 to eliminate the fraction:

\[ x \geq 28 \times 3 \]

Calculating that gives:

\[ x \geq 84 \]

Thus, the solution for the inequality is

\[ \boxed{x \geq 84} \]

6x + 7 greaterequal sign - 23

To solve the inequality

\[ 6x + 7 \geq -23, \]

follow these steps:

  1. Subtract 7 from both sides to isolate the term with \( x \):

\[ 6x + 7 - 7 \geq -23 - 7 \]

This simplifies to:

\[ 6x \geq -30. \]

  1. Divide both sides by 6 to solve for \( x \):

\[ x \geq \frac{-30}{6}. \]

Calculating that gives:

\[ x \geq -5. \]

Thus, the solution for the inequality is

\[ \boxed{x \geq -5}. \]