Solve for x and graph the solution on the number line below.
−7<−5x+3 or
−52≥−5x+3
To solve the first inequality, we can start by subtracting 3 from both sides of the equation:
-7 - 3 < -5x + 3 - 3
Simplifying this gives us:
-10 < -5x
Next, we can divide both sides of the equation by -5. Since we're dividing by a negative number, we need to reverse the inequality sign:
-10/-5 > -5x/-5
This simplifies to:
2 > x
So, the solution to the first inequality is x < 2.
To solve the second inequality, we can start by subtracting 3 from both sides of the equation:
-52 - 3 ≥ -5x + 3 - 3
Simplifying this gives us:
-55 ≥ -5x
Next, we can divide both sides of the equation by -5. Since we're dividing by a negative number, we need to reverse the inequality sign again:
-55/-5 ≤ -5x/-5
This simplifies to:
11 ≤ x
So, the solution to the second inequality is x ≥ 11.
Graphing these solutions on a number line, we have:
<-------|------------------------|----------------------|-------->
-∞ 2 11 +∞
what is this on a number line
On a number line, the solution would be represented by shading the interval between 2 and positive infinity (denoted by a filled-in circle on the number line at 2) and also shading the interval between negative infinity and 11 (denoted by a filled-in circle on the number line at 11). These shaded intervals represent all the values of x that satisfy the given inequalities.
wrong
Apologies for the incorrect response. Here is the correct representation on a number line:
<-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|------>
-∞ -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
For the first inequality, x < 2, the solution is all values of x less than 2, but not including 2. This can be represented by shading everything to the left of 2 on the number line.
For the second inequality, x ≥ 11, the solution is all values of x greater than or equal to 11. This can be represented by shading everything to the right of or including 11 on the number line.
Combining the two solutions, the shaded area on the number line would be everything to the left of 2, and everything to the right of or including 11.