Solving Equations

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What is the first step in solving a simple linear equation like 2x + 3 = 7?

Subtract 3 from both sides to isolate the term with the variable.

What does it mean to 'isolate the variable' in an equation?

It means rewriting the equation so that the variable is alone on one side of the equation.

Solve the equation: x/4 = 2.

Multiply both sides by 4 to get x = 8.

If you have the equation 3(x - 2) = 9, what should you do first?

Distribute the 3 to both terms inside the parentheses.

What is the solution to the equation 5x = 20?

Divide both sides by 5 to find x = 4.

True or False: You can add the same number to both sides of an equation to maintain balance.

True.

How can you check if your solution to an equation is correct?

Substitute your solution back into the original equation to see if both sides are equal.

Solve for y: y + 6 = 12.

Subtract 6 from both sides to find y = 6.

What operation would you use to solve x - 4 = 10?

Add 4 to both sides.

When solving -3x = 9, what should you do?

Divide both sides by -3 to get x = -3.

Why do you need to perform the same operation on both sides of an equation?

To keep the equation balanced and equality true.

What does 'equation' mean?

An equation is a statement that two expressions are equal, often containing variables.

Solve for x in the equation 6 + x = 10.

Subtract 6 from both sides to get x = 4.

If you start with 2(x + 3) = 10, what is the first step?

Divide both sides by 2 to simplify the equation to x + 3 = 5.

How would you solve the equation 7 - x = 4?

Subtract 7 from both sides and then multiply both sides by -1 to find x = 3.




Test Your Knowledge

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1. What is the first step in solving a simple linear equation like 2x + 3 = 7?

Multiply both sides by 2.

Divide both sides by 2.

Subtract 3 from both sides to isolate the term with the variable.

Add 3 to both sides to eliminate the constant.

2. What does it mean to 'isolate the variable' in an equation?

To multiply the variable by its coefficient.

To eliminate the exponent of the variable.

It means rewriting the equation so that the variable is alone on one side of the equation.

To combine like terms involving the variable.

3. Solve the equation: x/4 = 2.

Multiply both sides by 4 to get x = 8.

Add 4 to both sides to get x = 6.

Divide both sides by 2 to get x = 2.

Subtract 4 from both sides to get x = -2.

4. If you have the equation 3(x - 2) = 9, what should you do first?

Add 2 to both sides.

Distribute the 3 to both terms inside the parentheses.

Divide both sides by 3.

Subtract 3 from both sides.

5. What is the solution to the equation 5x = 20?

Add 5 to both sides to find x = 25.

Multiply both sides by 4 to find x = 80.

Subtract 5 from both sides to find x = 15.

Divide both sides by 5 to find x = 4.

6. True or False: You can add the same number to both sides of an equation to maintain balance.

True.

False.

Only if the number is positive.

Only if the equation is linear.

7. How can you check if your solution to an equation is correct?

Subtract the solution from both sides of the equation.

Substitute your solution back into the original equation to see if both sides are equal.

Multiply the solution by the coefficient of the variable.

Divide the solution by the number on the right side of the equation.

8. Solve for y: y + 6 = 12.

Add 6 to both sides to find y = 18.

Subtract 6 from both sides to find y = 6.

Multiply both sides by 6 to find y = 72.

Divide both sides by 6 to find y = 2.

9. What operation would you use to solve x - 4 = 10?

Multiply both sides by 4.

Add 4 to both sides.

Subtract 10 from both sides.

Divide both sides by 2.

10. When solving -3x = 9, what should you do?

Divide both sides by -3 to get x = -3.

Add 3 to both sides to get x = 12.

Subtract 9 from both sides to get x = 0.

Multiply both sides by -3 to get x = 27.

11. Why do you need to perform the same operation on both sides of an equation?

To keep the equation balanced and equality true.

To make sure the equation becomes quadratic.

To cancel out the negative terms.

To simplify the coefficients.

12. What does 'equation' mean?

An equation is a statement that two expressions are equal, often containing variables.

An equation is an inequality that only contains numbers.

An equation is a mathematical formula used only for algebra.

An equation is a set of operations performed in sequence.

13. Solve for x in the equation 6 + x = 10.

Add 6 to both sides to get x = 16.

Subtract 6 from both sides to get x = 4.

Multiply both sides by 6 to get x = 60.

Divide both sides by 2 to get x = 5.

14. If you start with 2(x + 3) = 10, what is the first step?

Add 3 to both sides to get x = 13.

Multiply both terms inside the parentheses by 2.

Divide both sides by 2 to simplify the equation to x + 3 = 5.

Subtract 6 from both sides to simplify.

15. How would you solve the equation 7 - x = 4?

Add x to both sides and then add 4.

Subtract 7 from both sides and then multiply both sides by -1 to find x = 3.

Add 7 to both sides to get x = 11.

Simply substitute x with 3 and check.