1/5(2x-10) + 4x = -3(1/5x + 4. Solve for x. I need some really help! please and thank you.
Ms.Sue?
1/5(2x-10) + 4x = -3(1/5x + 4)
first, get rid of those pesky fractions by multiplying by 5:
2x-10 + 20x = -3(x+20)
22x-10 = -3x - 60
25x = -50
x = -2
Thank you so much!
To solve the equation 1/5(2x-10) + 4x = -3(1/5x + 4) for x, we will follow these steps:
Step 1: Distribute the multipliers on both sides of the equation.
Step 2: Simplify any expressions within parentheses.
Step 3: Combine like terms on both sides.
Step 4: Isolate the variable term, x.
Step 5: Solve for x.
Now, let's go through each step in detail:
Step 1: Distribute the multipliers on both sides of the equation:
On the left side, distribute the multiplier 1/5 to both terms inside the parentheses:
(1/5)*(2x-10) = (1/5)*2x + (1/5)*(-10) = 2/5x - 2
On the right side, distribute the multiplier -3 to both terms inside the parentheses:
-3*(1/5x + 4) = -3*(1/5x) + (-3)*4 = -3/5x - 12
Now, the equation becomes: 2/5x - 2 + 4x = -3/5x - 12.
Step 2: Simplify any expressions within parentheses:
On the left side, there are no more parentheses.
On the right side, distribute -3 to 1/5x: -3/5 * x = -3/5x.
Now, the equation becomes: 2/5x - 2 + 4x = -3/5x - 12.
Step 3: Combine like terms on both sides:
Combine the x terms on the left side: 2/5x + 4x = 2/5x + 20/5x = (2 + 20)/5x = 22/5x.
Combine the constant terms on both sides: -2 - 12 = -14.
Now, the equation becomes: 22/5x - 14 = -3/5x.
Step 4: Isolate the variable term, x:
To isolate the 22/5x term, we need to move the -3/5x term to the left side of the equation.
Add 3/5x to both sides of the equation: (22/5x - 3/5x) - 14 = -14 + (3/5x - 3/5x).
Simplify: (22/5 - 3/5)x - 14 = -14.
Combine the x terms on the left side: (22/5 - 3/5)x = 19/5x.
Now, the equation becomes: 19/5x - 14 = -14.
Step 5: Solve for x:
To solve for x, we need to isolate the x term. Move the constant -14 to the right side of the equation.
Add 14 to both sides of the equation: (19/5x - 14) + 14 = -14 + 14.
Simplify: 19/5x = 0.
To solve for x, multiply both sides of the equation by the reciprocal of 19/5, which is 5/19:
(19/5x) * (5/19) = 0 * (5/19).
Simplify: x = 0.
Therefore, the solution to the equation is x = 0.