Question

solve the inequality and graph the solution.

$u + 10 < 19$

to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.

number line with ticks at 0,1,2,3,4,5,6

Explanation:

Step1: Subtract 10 from both sides

To solve the inequality \( u + 10 < 19 \), we subtract 10 from both sides of the inequality. This is based on the subtraction property of inequalities, which states that if we subtract the same number from both sides of an inequality, the inequality sign remains the same.

$$ u + 10 - 10 < 19 - 10 $$

Step2: Simplify both sides

Simplifying the left - hand side, \( u+10 - 10=u \). Simplifying the right - hand side, \( 19 - 10 = 9 \). So we get \( u<9 \).

For graphing the solution:

• The solution to the inequality \( u < 9 \) on the number line: We use an open circle at \( u = 9 \) (because the inequality is strict, \( u\) is not equal to 9) and draw a ray to the left of 9 to represent all the numbers less than 9. But looking at the given number line (with markings up to 6), we can see that the scale might be different from what is shown here. However, the algebraic solution for the inequality \( u + 10<19 \) is \( u < 9 \).

Answer:

The solution to the inequality \( u + 10<19 \) is \( u<9 \). For graphing, place an open circle at 9 (if the number line is extended to 9) and draw a ray pointing to the left.