Question

Sketch the graph of the inequality in a coordinate plane. $$ x+3<4 $$

Short answer

The graph of the inequality \(x+3<4\) is a line extending from the point x=1 towards lesser values on the x-axis, with an open circle at x=1 to indicate that this point is not included in the set of solutions.

Step-by-step solution

Solve the Inequality for x

To solve the inequality for x, first subtract 3 from both sides of the inequality: \(x+3-3 < 4-3\)This simplifies to: \(x<1\)

Determine Which Values of x Satisfy the Inequality

According to the inequality, any value of x that is less than 1 will satisfy the inequality.

Sketch the Graph

To sketch the graph in a coordinate plane, draw a number line (the x-axis) and mark the point at x=1. Since the inequality is 'less than' and not 'less than or equal to', use an open circle to indicate that the point at x=1 is not included in the set of solutions. Draw a line extending to the left from x=1 to indicate that all values less than 1 are included in the set of solutions.