Linear Equations with Fractions Worksheet

Linear equations with fractions can be challenging for many students. Understanding how to solve these types of equations requires a solid understanding of both the mathematical properties of fractions and how to manipulate equations using variables. If you're a student who needs practice in this area or a teacher looking for a resource to support your lessons, this Linear Equations with Fractions Worksheet is a valuable tool to help solidify your understanding of this topic.

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Write the equation of a line in slope-intercept form using fractions.

To write the equation of a line in slope-intercept form using fractions, you would write it as y = mx + b, where m is the slope of the line (a fraction like 3/5, for example) and b is the y-intercept (a fraction like 1/4, for example). So, an example of a line in slope-intercept form with fractions could be y = (3/5)x + (1/4).

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

To solve the equation (3/4)x - 5 = 2/3, first isolate the variable x. Add 5 to both sides of the equation to get (3/4)x = 2/3 + 5. Then find a common denominator to add 2/3 and 5, which is 15. Therefore, 2/3 + 5 = 2/3 + 15/3 = 17/3. So now the equation becomes (3/4)x = 17/3. To solve for x, multiply both sides by the reciprocal of (3/4), which is 4/3. This gives x = (17/3) * (4/3) = 68/9, or x = 7.56 (rounded to two decimal places). Thus, the solution to the equation is x = 68/9 or x ? 7.56.

Find the solution to the system of equations: 2x/3 + 1/2y = 5/6 and x/5 - y/4 = 7/10.

The solution to the system of equations is x = 2, y = 4.

Graph the linear equation: y = -2/5x + 3.

To graph the linear equation y = -2/5x + 3, start by plotting the y-intercept at 3 on the y-axis. Then, use the slope of -2/5 to find a second point by moving down 2 units and to the right 5 units, and plot that point. Connect the two points to draw a straight line. This line represents the graph of the linear equation y = -2/5x + 3.

Simplify the expression: (2/3)(3/8) - (1/4)(5/6).

To simplify the expression (2/3)(3/8) - (1/4)(5/6), we first multiply the fractions within the parentheses: (2/3)(3/8) = 6/24 and (1/4)(5/6) = 5/24. Subtracting these two results gives 6/24 - 5/24 = 1/24. Therefore, the simplified expression is 1/24.

Solve for x: (4/5)(2x - 1) = 3/4.

To solve for x, first distribute the 4/5 on the left side, giving you (8/5)x - 4/5 = 3/4. Then, add 4/5 to both sides to isolate the x term, resulting in (8/5)x = 3/4 + 4/5. Now, find a common denominator to add the fractions on the right side, which would be 20, so 3/4 + 4/5 = 15/20 + 16/20 = 31/20. Finally, multiply both sides by 5/8 to solve for x, leading to x = (31/20) * 5/8 = 31/32. Thus, the solution for x is 31/32.

Determine the slope of the line passing through the points (-3, 1) and (2, -4) using fractions.

To determine the slope of the line passing through the points (-3, 1) and (2, -4) using fractions, we use the formula for slope which is (y2 - y1) / (x2 - x1). By substituting the coordinates of the points into the formula, we get (-4 - 1) / (2 - (-3)) = -5 / 5 = -1. Therefore, the slope of the line passing through the points (-3, 1) and (2, -4) is -1.

Rewrite the equation 2x - 3y = 7 in slope-intercept form.

To rewrite the equation 2x - 3y = 7 in slope-intercept form, we need to solve for y. By isolating y, we get y = (2/3)x - 7/3. Therefore, the equation in slope-intercept form is y = (2/3)x - 7/3.

Solve the inequality: (1/2)x + (3/4) > 1/3.

To solve the inequality (1/2)x + (3/4) > 1/3, first simplify the left side by finding a common denominator, giving us (2/4)x + (3/4) > 1/3. Combining the fractions, we get (5/4)x > 1/3. Multiplying both sides by (4/5) to isolate x, we have x > 4/15. Therefore, the solution to the inequality is x > 4/15.

Find the x-intercept of the line represented by the equation 2/3x - 4y = 8.

To find the x-intercept of the line represented by the equation 2/3x - 4y = 8, we need to substitute y with 0 in the equation. This gives us 2/3x - 4(0) = 8, simplifying to 2/3x = 8. Solving for x, we get x = 12. Therefore, the x-intercept of the line is 12.