Solve the following equations.Check your result in each case
`5(2X-3)-3(3X-7)=5`

Answer

To solve the equation \(5(2X-3)-3(3X-7)=5\), we will follow these steps:

### Step 1: Expand the equation
We start by distributing the constants outside the brackets to the terms inside the brackets.

\[ 5(2X - 3) - 3(3X - 7) = 5 \]

Expanding this gives:

\[ 5 \cdot 2X - 5 \cdot 3 - 3 \cdot 3X + 3 \cdot 7 = 5 \]

Calculating each term:

\[ 10X - 15 - 9X + 21 = 5 \]

### Step 2: Combine like terms
Now, we will combine the \(X\) terms and the constant terms on the left side of the equation.

\[ (10X - 9X) + (-15 + 21) = 5 \]

This simplifies to:

\[ 1X + 6 = 5 \]

### Step 3: Isolate the variable
Next, we will isolate \(X\) by moving the constant term to the right side of the equation.

\[ 1X = 5 - 6 \]

Calculating the right side gives:

\[ 1X = -1 \]

### Step 4: Solve for \(X\)
Thus, we find:

\[ X = -1 \]

### Step 5: Check the solution
To verify our solution, we will substitute \(X = -1\) back into the original equation.

Substituting \(X = -1\):

\[ 5(2(-1) - 3) - 3(3(-1) - 7) = 5 \]

Calculating inside the brackets:

\[ 5(-2 - 3) - 3(-3 - 7) = 5 \]

This simplifies to:

\[ 5(-5) - 3(-10) = 5 \]

Calculating further:

\[ -25 + 30 = 5 \]

Finally, we find:

\[ 5 = 5 \]

Since both sides of the equation are equal, our solution is verified.

### Final Answer
\[ X = -1 \]

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