Question

1. solve: -2(4x + 3) - (x - 7) = 46

Explanation:

Step1: Expand the brackets

First, we use the distributive property (also known as the distributive law) to expand \(-2(4x + 3)\) and \(-(x - 7)\).

For \(-2(4x + 3)\), we multiply \(-2\) by each term inside the brackets: \(-2\times4x=-8x\) and \(-2\times3 = -6\).

For \(-(x - 7)\), we can think of it as \(-1\times(x - 7)\), so multiplying \(-1\) by each term inside the brackets gives \(-1\times x=-x\) and \(-1\times(-7) = 7\).

Putting it all together, the original equation \(-2(4x + 3)-(x - 7)=46\) becomes:

\(-8x - 6 - x + 7 = 46\)

Step2: Combine like terms

Next, we combine the \(x\)-terms and the constant terms.

For the \(x\)-terms: \(-8x - x=-9x\)

For the constant terms: \(-6 + 7 = 1\)

So the equation simplifies to:

\(-9x + 1 = 46\)

Step3: Isolate the variable term

We want to get the term with \(x\) by itself. To do this, we subtract \(1\) from both sides of the equation.

Subtracting \(1\) from both sides:

\(-9x + 1 - 1=46 - 1\)

Simplifying both sides:

\(-9x=45\)

Step4: Solve for \(x\)

Now, we solve for \(x\) by dividing both sides of the equation by \(-9\).

Dividing both sides by \(-9\):

\(x=\frac{45}{-9}\)

Simplifying the right-hand side:

\(x = - 5\)

Answer:

\(x=-5\)