4>-3+3 or 6<or equal -2x+3 solve the inequality
To solve the inequality 4 > -3 + 3, we first simplify the expression on the right side of the inequality:
-3 + 3 = 0
Now we have the inequality 4 > 0. Since 4 is greater than 0, the inequality is true for all real numbers.
Moving on to the second inequality, 6 ≤ -2x + 3, we need to isolate the variable on one side of the inequality sign. Let's do that step-by-step:
6 ≤ -2x + 3
Subtract 3 from both sides:
6 - 3 ≤ -2x
3 ≤ -2x
Divide both sides by -2, remember when you divide by a negative number, the inequality sign flips:
3 / -2 ≥ x
-3/2 ≥ x
So the solution to the inequality is x ≤ -3/2. This means that any value of x that is less than or equal to -3/2 will make the inequality true.
To solve the inequality 4 > -3 + 3 or 6 ≤ -2x + 3, we will simplify the expressions and solve them separately.
Step 1: Simplify the expressions.
-3 + 3 equals 0, so the first inequality becomes 4 > 0.
Step 2: Analyze the first inequality.
Since 4 is greater than 0, this inequality is always true. Therefore, the first part of the compound inequality (4 > 0) is always true.
Step 3: Simplify the second expression.
-2x + 3 is already simplified.
Step 4: Analyze the second inequality.
6 is less than or equal to -2x + 3, so we can subtract 3 from both sides to isolate -2x.
6 - 3 ≤ -2x + 3 - 3
3 ≤ -2x
Then, divide both sides by -2, remembering to flip the inequality symbol since we're multiplying/dividing by a negative number:
3 / -2 ≥ -2x / -2
-3/2 ≥ x
So, the second inequality can be rewritten as x ≤ -3/2.
Step 5: Combine the results.
Since the first inequality (4 > 0) is always true and the second inequality (x ≤ -3/2) is a specific condition, the solution to the entire compound inequality is:
4 > 0 or x ≤ -3/2