Two-Step Equations with Fractions Worksheet
Are you a middle or high school student struggling to solve two-step equations involving fractions? Look no further! This worksheet will guide you through practicing this specific type of equation, helping you build confidence and improve your problem-solving skills.
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Solve the equation: 2/3x - 1/5 = 4
To solve the equation, first add 1/5 to both sides to isolate the term with x. This gives you 2/3x = 4 + 1/5. Simplify the right side to get 2/3x = 21/5. Then multiply both sides by 3/2 to solve for x, which gives x = (21/5) * (3/2) = 63/10. Therefore, the solution to the equation 2/3x - 1/5 = 4 is x = 63/10.
Solve the equation: 3/4x + 2/3 = 1
To solve the equation 3/4x + 2/3 = 1, first, find a common denominator for 4 and 3, which is 12. Then, rewrite the equation as 9/12x + 8/12 = 12/12. Simplifying the equation gives 9/12x = 4/12. Divide both sides by 9/12 to isolate x, which yields x = 4/12 ÷ 9/12 = 4/12 * 12/9 = 4/9. Therefore, the solution to the equation 3/4x + 2/3 = 1 is x = 4/9.
Solve the equation: 5/6x - 3/8 = 2/5
To solve the equation 5/6x - 3/8 = 2/5, first find a common denominator for all fractions, which is 24. Then, rewrite each fraction with the common denominator: 20/24x - 9/24 = 9/24. Next, combine like terms to get 20/24x - 9/24 = 9/24. 20/24x = 18/24. Finally, solve for x by dividing both sides by 20/24: x = (18/24) / (20/24) = 18/24 * 24/20 = 18/20 = 9/10. Therefore, the solution to the equation is x = 9/10.
Solve the equation: 1/2x + 3/4 = 2
To solve the equation 1/2x + 3/4 = 2, we first need to isolate x. We can do this by subtracting 3/4 from both sides to get 1/2x = 5/4. Then, we multiply both sides by 2 to get x = 5/2 or x = 2.5. Hence, the solution to the equation is x = 2.5.
Solve the equation: 4/7x - 5/9 = 3/5
To solve the equation 4/7x - 5/9 = 3/5, we first find a common denominator for the fractions on the left side. The common denominator is 63. So, rewriting the equation with this common denominator, we get 36/63x - 35/63 = 37/63. Combining like terms, we have 36/63x - 35/63 = 37/63 ? 1/63x = 72/63. Now, solving for x by multiplying both sides by 63, x = 72. Therefore, the solution for the equation is x = 72.
Solve the equation: 7/8x + 2/3 = 1/4
To solve the equation 7/8x + 2/3 = 1/4, first subtract 2/3 from both sides to isolate the x-term. This gives 7/8x = 1/4 - 2/3. Find a common denominator for 1/4 and 2/3, which is 12. Therefore, the equation becomes 7/8x = 3/12 - 8/12. Simplifying this further gives 7/8x = -5/12. To solve for x, multiply both sides by the reciprocal of 7/8, which is 8/7. Therefore, x = (-5/12) * (8/7) = -40/84 or -20/42 when simplified further.
Solve the equation: 2/5x - 1/3 = 3/7
To solve the equation 2/5x - 1/3 = 3/7, we first need to simplify the equation by finding a common denominator. The common denominator for 5, 3, and 7 is 105. Therefore, we rewrite the equation as 42/105x - 35/105 = 45/105. By combining like terms, we get 42/105x - 35/105 = 45/105, which simplifies to 7/105x = 10/105. Dividing by 7/105, we get x = 10/7. Thus, the solution to the equation is x = 10/7.
Solve the equation: 3/4x + 1/2 = 5/6
To solve the equation 3/4x + 1/2 = 5/6, we first need to get rid of the fractions by finding a common denominator, which in this case is 12. Multiplying each term by 12, we get 9x + 6 = 10. Then, by isolating the variable x, we subtract 6 from both sides to get 9x = 4, and finally, divide by 9 on both sides to solve for x, yielding x = 4/9.
Solve the equation: 1/3x - 1/4 = 2/5
To solve the equation 1/3x - 1/4 = 2/5, first find a common denominator, which is 60 in this case. Multiply each term by 60 to clear the fractions, resulting in 20x - 15 = 24. Then, isolate the variable term by adding 15 to both sides to get 20x = 39. Finally, divide by 20 to solve for x, getting x = 39/20 or x = 1.95.
Solve the equation: 2/9x + 3/5 = 4/7
To solve the equation 2/9x + 3/5 = 4/7, first find a common denominator for the fractions, which is 315. Rewrite the equation as 70/315x + 189/315 = 180/315. Combine like terms to get 70x + 189 = 180. Now, isolate the variable by subtracting 189 from both sides, giving 70x = -9. Finally, divide by 70 to solve for x, obtaining x = -9/70.
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