Equations Review

Front

What is the process to isolate a variable in a linear equation?

Back

To isolate a variable in a linear equation, perform inverse operations on both sides of the equation to get the variable by itself. This may involve adding, subtracting, multiplying, or dividing both sides by the same number.

Front

How do you solve the equation 113 - c = 244 for c?

Back

To solve for c, subtract 113 from both sides: -c = 244 - 113. This simplifies to -c = 131. Then, multiply both sides by -1 to get c = -131.

Front

What is the solution to the equation \( \frac{7}{2}m = 49 \)?

Back

To solve for m, multiply both sides by the reciprocal of \( \frac{7}{2} \), which is \( \frac{2}{7} \): m = 49 * \( \frac{2}{7} \) = 14.

Front

How do you solve the equation 5x - 4 + 2x = 3?

Back

Combine like terms: 7x - 4 = 3. Then, add 4 to both sides: 7x = 7. Finally, divide both sides by 7 to get x = 1.

Front

What is the solution to the equation \( \frac{u}{2} - 9 = 29 \)?

Back

To solve for u, first add 9 to both sides: \( \frac{u}{2} = 29 + 9 \), which simplifies to \( \frac{u}{2} = 38 \). Then, multiply both sides by 2 to get u = 76.

Front

How do you solve the equation -4 + w = -6 for w?

Back

To solve for w, add 4 to both sides: w = -6 + 4, which simplifies to w = -2.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

What does it mean to perform inverse operations in solving equations?

Back

Inverse operations are operations that undo each other. For example, addition and subtraction are inverse operations, as are multiplication and division.

Front

What is the importance of checking your solution in an equation?

Back

Checking your solution ensures that the value you found satisfies the original equation, confirming that your solution is correct.

Front

What is the first step in solving an equation like 2x + 3 = 11?

Back

The first step is to isolate the term with the variable by subtracting 3 from both sides: 2x = 11 - 3.