solve 9/10(3x+2x)+2 >_ 23

To solve the inequality \( \frac{9}{10}(3x+2x)+2 >_ 23\), we'll follow these steps:

Step 1: Simplify the left side of the equation.
To simplify the equation, we need to distribute the \(\frac{9}{10}\) to the terms inside the parentheses.
\(\frac{9}{10}(3x+2x)+2 >_ 23\)
\(\frac{9}{10} \cdot 3x + \frac{9}{10} \cdot 2x + 2 >_ 23\)
\(\frac{27}{10}x + \frac{18}{10}x + 2 >_ 23\)
\(\frac{45}{10}x + 2 >_ 23\)

Step 2: Combine the like terms.
The terms \(\frac{45}{10}x\) and \(\frac{18}{10}x\) can be combined.
\(\frac{63}{10}x + 2 >_ 23\)

Step 3: Isolate the variable.
We want to isolate the variable term, which is \(\frac{63}{10}x\), by moving the constant term, which is 2, to the other side of the inequality symbol.
\(\frac{63}{10}x >_ 23 - 2\)
\(\frac{63}{10}x >_ 21\)

Step 4: Solve for x.
To solve for x, we need to divide both sides of the inequality by \(\frac{63}{10}\). Remember, when dividing an inequality by a negative number, the direction of the inequality should be reversed.
\(\frac{\frac{63}{10}x}{\frac{63}{10}} <_ \frac{21}{\frac{63}{10}}\)
\(x <_ \frac{21}{\frac{63}{10}}\)
\(x <_ \frac{21}{\frac{63}{10}} \cdot \frac{10}{10}\)
\(x <_ \frac{210}{63}\)
\(x <_ \frac{10}{3}\)

So, the solution to the inequality \( \frac{9}{10}(3x+2x)+2 >_ 23\) is \( x <_ \frac{10}{3} \).