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Question Solve the equation 3(2u−1)+4u+3=4(u+5)+2u3(2u-1)+4u+3=4(u+5)+2u. Express the solution uu as an integer or simplified fraction.

Studdy Solution

STEP 1

Assumptions
1. The equation to solve is 3(2u−1)+4u+3=4(u+5)+2u3(2u-1) + 4u + 3 = 4(u+5) + 2u.
2. We need to find the value of uu that satisfies the equation.
3. The solution should be expressed as an integer or a simplified fraction.

STEP 2

Distribute the multiplication over addition in the terms 3(2u−1)3(2u-1) and 4(u+5)4(u+5).
3(2u−1)=3⋅2u−3⋅1=6u−33(2u-1) = 3 \cdot 2u - 3 \cdot 1 = 6u - 3 4(u+5)=4⋅u+4⋅5=4u+204(u+5) = 4 \cdot u + 4 \cdot 5 = 4u + 20

STEP 3

Rewrite the equation with the distributed terms.
6u−3+4u+3=4u+20+2u6u - 3 + 4u + 3 = 4u + 20 + 2u

STEP 4

Combine like terms on both sides of the equation.
On the left side, combine 6u6u and 4u4u, and combine −3-3 and +3+3. On the right side, combine 4u4u and 2u2u.
10u=6u+2010u = 6u + 20

STEP 5

Subtract 6u6u from both sides of the equation to get all the uu terms on one side.
10u−6u=6u+20−6u10u - 6u = 6u + 20 - 6u

STEP 6

Simplify both sides of the equation.
4u=204u = 20

STEP 7

Divide both sides of the equation by 4 to solve for uu.
4u4=204\frac{4u}{4} = \frac{20}{4}

STEP 8

Simplify the equation to find the value of uu.
u=5u = 5
The solution to the equation is u=5u = 5.

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