How would I solve these problem?
4/x-1 = 10/1
and
x/x-8 = x / 24
1. 4/(x-1) = 10/1.
Invert both sides:
(x-1)/4 = 1/10
Multiply both sides by 40:
10(x-1) = 4.
10x - 10 = 4.
10x = 14.
X = 14/10 = 7/5.
2. x/(x-8) = x/24.
Multiply both sides by 24:
24x/(x-8) = x.
Cross multiply:
x(x-8) = 24x.
x^2 -8x = 24x.
x^2 - 8x - 24x = 0.
x^2 - 32x = 0.
x(x-32) = 0.
X = 0.
x-32 = 0.
X = 32.
Solution set: X = 0, and X = 32.
8x24
To solve these equations, we need to isolate the variable x by performing the necessary operations. Let's go step by step.
Equation 1: 4(x - 1) = 10(1)
1. Distribute on both sides to eliminate the parentheses:
4x - 4 = 10
2. Add 4 to both sides to get the constant terms on one side:
4x - 4 + 4 = 10 + 4
4x = 14
3. Divide both sides by 4 to solve for x:
4x/4 = 14/4
x = 3.5
Therefore, the solution to the equation 4/(x - 1) = 10/1 is x = 3.5.
Equation 2: x/(x - 8) = x/24
1. Cross multiply to eliminate the fractions:
24x = x(x - 8)
2. Expand the right side by multiplying x with both terms inside the parentheses:
24x = x^2 - 8x
3. Move all terms to the left side to form a quadratic equation:
x^2 - 8x - 24x = 0
x^2 - 32x = 0
4. Factor out x from the equation:
x(x - 32) = 0
5. Set each factor equal to zero and solve for x:
x = 0 OR x - 32 = 0
x = 0 OR x = 32
Therefore, the solutions to the equation x/(x - 8) = x/24 are x = 0 and x = 32.