Multi-Step Equations with Fractions Worksheet

Are you a middle school or high school student struggling with multi-step equations involving fractions? Look no further, as we have the perfect solution for you! Our Multi-Step Equations with Fractions Worksheet is designed to help you practice and master this important concept in algebra. In this worksheet, you will encounter various equations that require multiple steps to solve, all while working with fractions. Whether you are new to this topic or just need some extra practice, this worksheet will provide you with the practice you need to succeed.

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Solve the equation: 2/3(x - 4) = 8/9

To solve the equation 2/3(x - 4) = 8/9, first simplify by distributing the 2/3 to the terms inside the parentheses, giving you 2/3x - 8/3 = 8/9. Next, add 8/3 to both sides to isolate the variable term, resulting in 2/3x = 8/9 + 8/3. Then, find a common denominator for the fractions on the right side, which gives you 2/3x = 8/9 + 24/9 = 32/9. Finally, multiply both sides by 3/2 to solve for x, which yields x = (32/9) * (3/2) = 16/3. Therefore, the solution to the equation is x = 16/3.

Solve the equation: 5/6(2x + 3) = 1/2

To solve the equation 5/6(2x + 3) = 1/2, we first distribute the 5/6 to both terms inside the parentheses, resulting in 10x/6 + 15/6 = 1/2. This simplifies to 10x/6 + 15/6 = 3/6. Combining like terms gives 10x/6 + 15/6 = 3/6, which simplifies to 10x + 15 = 3. Subtracting 15 from both sides gives 10x = -12. Finally, dividing both sides by 10 gives x = -1.2. Therefore, the solution to the equation is x = -1.2.

Solve the equation: 3/4(5x + 2) - 1/6 = 11/12

To solve the equation 3/4(5x + 2) - 1/6 = 11/12, first distribute the 3/4 to 5x and 2: 15x/4 + 6/4 - 1/6 = 11/12. Next, find a common denominator for all fractions to simplify: 90(15x) +90(6) - 15 = 45. This simplifies to 60x + 45 - 15 = 45. Combining like terms gives 60x + 30 = 45. Subtracting 30 from both sides gives 60x = 15. Finally, dividing by 60 gives x = 1/4.

Solve the equation: 7/8(x - 1/4) + 1/3 = 5/6

To solve the equation 7/8(x - 1/4) + 1/3 = 5/6, first distribute the 7/8 to the terms inside the parentheses to get 7/8*x - 7/32 + 1/3 = 5/6. Next, combine the constant terms to get 7/8*x - 7/32 + 10/32 = 5/6. Simplify further to get 7/8*x + 3/32 = 5/6. Move the constant term 3/32 to the other side by subtracting it from both sides to get 7/8*x = 5/6 - 3/32. Further simplify to get 7/8*x = 40/48 - 9/48 = 31/48. Finally, divide by 7/8 to get x = 31/48 * 8/7 = 31/42 = 1/1.42 or approximately x = 0.704.

Solve the equation: 4/5(3x + 1) - 1/10 = 2/3

To solve the equation, first distribute the 4/5 to 3x and 1: (4/5)*3x + (4/5)*1 - 1/10 = 2/3. This simplifies to 12/5x + 4/5 - 1/10 = 2/3. Next, combine the constants on the left side: 12/5x + 4/5 - 1/10 = 2/3 simplifies to 12/5x + 39/10 = 2/3. Then, subtract 39/10 from both sides to isolate the term with x: 12/5x = 2/3 - 39/10. This further simplifies to 12/5x = 20/30 - 117/30 = -97/30. Finally, to solve for x, divide both sides by 12/5: x = -97/30 * 5/12 = -97/6 or -16.17. Therefore, x = -16.17.

Solve the equation: 2/3(4x - 1) + 1/2 = 3/4

To solve the equation 2/3(4x - 1) + 1/2 = 3/4, first distribute the 2/3 to 4x and -1, then combine like terms to simplify the equation. This gives us (8x/3) - 2/3 + 1/2 = 3/4. Next, convert 1/2 to have a common denominator of 3, which becomes 3/6. Therefore, the equation simplifies to (8x/3) - 2/3 + 3/6 = 3/4. Further simplify to get (8x/3) - 2/3 + 1/2 = 3/4. To find x, isolate the variable by subtracting (-2/3 + 3/6) from both sides to get (8x/3) = 3/4 + 2/3 - 3/6, and finally solve for x to get x = 5/4.

Solve the equation: 3/4(x + 2/5) - 1/3 = 5/6

To solve the equation 3/4(x + 2/5) - 1/3 = 5/6, first distribute the 3/4 to both terms inside the parentheses, which gives you 3/4 * x + 3/4 * 2/5 - 1/3 = 5/6. This simplifies to 3/4x + 6/20 - 1/3 = 5/6. Next, find a common denominator for 20 and 3, which is 60. Rearrange the equation to clear the fractions and solve for x, which yields x = 10.

Solve the equation: 5/6(3x + 1/2) = 4/9

To solve the given equation, first distribute 5/6 to 3x and 1/2. This gives us 5/6 * 3x = 15/6x and 5/6 * 1/2 = 5/12. The equation now becomes 15/6x + 5/12 = 4/9. Next, we can combine the terms on the left side by finding a common denominator, which is 12. Thus, we have 30/12x + 5/12 = 4/9. To further simplify, we can combine the terms on the left side to get 35/12x = 4/9 - 5/12 = 16/36 - 15/36 = 1/36. Finally, by multiplying both sides by the reciprocal of 35/12, which is 12/35, we get x = (1/36) * (12/35) = 1/126. Therefore, the solution to the equation is x = 1/126.

Solve the equation: 1/3(2x - 1) + 1/5 = 2/3

To solve the equation 1/3(2x - 1) + 1/5 = 2/3, we first distribute the 1/3 to 2x and -1, yielding 2/3x - 1/3 + 1/5 = 2/3. Then, we combine like terms and find a common denominator to add fractions, resulting in 2/3x + 2/15 = 2/3. Next, we isolate x by subtracting 2/15 from both sides, obtaining 2/3x = 2/3 - 2/15. Simplifying further, we get 2/3x = 8/15, and then by dividing both sides by 2/3, we find x = 8/15 ÷ 2/3, which simplifies to x = 4/5. Thus, the solution to the equation is x = 4/5.

Solve the equation: 2/5(5x + 1/3) - 3/4 = 1/2

To solve the equation 2/5(5x + 1/3) - 3/4 = 1/2, first distribute the 2/5 to both terms inside the parentheses: 2(5/5)x + 2(1/3)/5 - 3/4 = 1/2. This simplifies to 2x + 2/15 - 3/4 = 1/2. Next, combine like terms to get 2x + 2/15 - 9/12 = 1/2. Simplifying further, we get 2x + 2/15 - 45/60 = 1/2, which can be simplified to 2x + 2/15 - 3/4 = 1/2. Finally, solve for x: 2x = 1/2 - 2/15 + 3/4. By calculating the values, we find that x = 13/20.