Solve for x.
Graph the solution.
5x+1<4x-3
To solve for x, we can start by subtracting 4x from both sides of the inequality to isolate the x term:
5x + 1 - 4x < 4x - 3 - 4x
This simplifies to:
x + 1 < -3
Next, we can subtract 1 from both sides of the inequality:
x + 1 - 1 < -3 - 1
This simplifies to:
x < -4
The solution for x is x < -4.
To graph the solution, we can draw a number line and label an open circle at -4 to represent that -4 is not included in the solution. Then, shade to the left of -4 to represent all the x values that satisfy the inequality.
To solve the inequality 5x + 1 < 4x - 3, we need to isolate the variable x on one side of the inequality sign.
Step 1: Move all the x terms to one side of the inequality.
5x - 4x + 1 < -3
Simplifying the equation, we have:
x + 1 < -3
Step 2: Move the constant term to the other side of the inequality.
x + 1 - 1 < -3 - 1
Simplifying the equation further, we have:
x < -4
The solution to the inequality is x < -4.
To graph this solution on a number line, draw a line with a point labeled -4 and a shaded area to the left of that point, indicating all the values of x that are less than -4.
To solve the inequality 5x + 1 < 4x - 3, we need to isolate the variable x. Here are the steps to solve it:
Step 1: Subtract 4x from both sides of the inequality:
5x + 1 - 4x < 4x - 3 - 4x
x + 1 < -3
Step 2: Subtract 1 from both sides of the inequality:
x + 1 - 1 < -3 - 1
x < -4
The solution to the inequality is x < -4.
Now, let's graph the solution on a number line to better visualize it:
Start by drawing a number line, with zero (0) in the middle, and positive numbers to the right and negative numbers to the left.
To represent x < -4, you can place an open circle at -4 on the number line to indicate that -4 is not included in the solution set, and then draw an arrow going to the left to show that all values less than -4 are included.
----------------------o---<------------------- (-∞, -4)
Here, the open circle at -4 indicates that -4 is not part of the solution, and the arrow to the left shows that the numbers less than -4 are part of the solution set.
That represents the graph of the solution to the inequality 5x + 1 < 4x - 3.