Solve each equation for x. 2(x-a) +b =3x+a

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Start by expanding the left side of the equation: \$2(x - a) + b = 3x + a$ becomes $2x - 2a + b = 3x + a$.

Next, get all terms involving $x$ on one side and constants on the other side. Subtract \$2x$ from both sides: $-2a + b = 3x - 2x + a$ which simplifies to $-2a + b = x + a$.

Then, isolate $x$ by subtracting $a$ from both sides: $-2a + b - a = x$ which simplifies to $-3a + b = x$.

Rewrite the equation to express $x$ explicitly: $x = -3a + b$.

This gives the solution for $x$ in terms of $a$ and $b$.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Distributive Property

The distributive property allows you to multiply a single term by each term inside parentheses. For example, 2(x - a) becomes 2*x - 2*a. This step is essential to simplify expressions and solve equations involving parentheses.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This simplifies the equation and makes it easier to isolate the variable. For instance, terms with x can be combined on one side.

Solving Linear Equations

Solving linear equations means finding the value of the variable that makes the equation true. This involves isolating x by performing inverse operations such as addition, subtraction, multiplication, or division on both sides of the equation.

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