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The solution of inequality 4x + 3 < 5x + 7 when x is a real number is
- a)[4, ∞)
- b)(-∞, 4)
- c)(-4,∞)
- d)None of the these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The solution of inequality 4x + 3 < 5x + 7 when x is a real number ...
4x + 3 < 5x + 7
subtract 4 both sides,
4x + 3 - 3 < 5x + 7 - 3
⇒ 4x < 5x + 4
subtract ' 5x ' both sides ,
[ equal number may be subtracted from both sides of an inequality without affecting the sign of inequality]
4x - 5x < 5x + 4 - 5
-x < 4
now, multiple with (-1) then, sign of inequality change .
-x.(-1) > 4(-1)
x > -4
hence, x€ ( -4 , ∞)
subtract 4 both sides,
4x + 3 - 3 < 5x + 7 - 3
⇒ 4x < 5x + 4
subtract ' 5x ' both sides ,
[ equal number may be subtracted from both sides of an inequality without affecting the sign of inequality]
4x - 5x < 5x + 4 - 5
-x < 4
now, multiple with (-1) then, sign of inequality change .
-x.(-1) > 4(-1)
x > -4
hence, x€ ( -4 , ∞)
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The solution of inequality 4x + 3 < 5x + 7 when x is a real number ...
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The solution of inequality 4x + 3 < 5x + 7 when x is a real number ...
Solution:
To solve the inequality 4x + 3 < 5x="" +="" 7,="" we="" need="" to="" isolate="" the="" variable="" x="" on="" one="" side="" of="" the="" inequality="" sign.="" />
Step 1: Subtract 4x from both sides of the inequality to eliminate the x term on the right side:
4x - 4x + 3 < 5x="" -="" 4x="" +="" />
3 < x="" +="" />
Step 2: Subtract 7 from both sides of the inequality to isolate the x term on the right side:
3 - 7 < x="" +="" 7="" -="" />
-4 < />
Step 3: Rewrite the inequality with x on the left side:
x > -4
The solution to the inequality is x > -4, which means that x can take on any real value greater than -4.
Explanation:
The inequality 4x + 3 < 5x="" +="" 7="" represents="" a="" linear="" inequality="" with="" an="" inequality="" sign="" /><) indicating="" that="" the="" left="" side="" is="" less="" than="" the="" right="" side.="" to="" solve="" this="" inequality,="" we="" need="" to="" manipulate="" the="" equation="" to="" isolate="" the="" variable="" x="" on="" one="" side.="">
By subtracting 4x from both sides, we eliminate the x term on the right side and obtain 3 < x="" +="" 7.="" next,="" we="" subtract="" 7="" from="" both="" sides="" to="" isolate="" the="" x="" term="" on="" the="" right="" side,="" resulting="" in="" -4="" />< x.="" />
To express the solution in a more familiar form, we rewrite the inequality with x on the left side as x > -4. This means that x can take on any real value greater than -4.
Therefore, the correct answer is option 'C' (-4, ) which represents all real numbers greater than -4.
To solve the inequality 4x + 3 < 5x="" +="" 7,="" we="" need="" to="" isolate="" the="" variable="" x="" on="" one="" side="" of="" the="" inequality="" sign.="" />
Step 1: Subtract 4x from both sides of the inequality to eliminate the x term on the right side:
4x - 4x + 3 < 5x="" -="" 4x="" +="" />
3 < x="" +="" />
Step 2: Subtract 7 from both sides of the inequality to isolate the x term on the right side:
3 - 7 < x="" +="" 7="" -="" />
-4 < />
Step 3: Rewrite the inequality with x on the left side:
x > -4
The solution to the inequality is x > -4, which means that x can take on any real value greater than -4.
Explanation:
The inequality 4x + 3 < 5x="" +="" 7="" represents="" a="" linear="" inequality="" with="" an="" inequality="" sign="" /><) indicating="" that="" the="" left="" side="" is="" less="" than="" the="" right="" side.="" to="" solve="" this="" inequality,="" we="" need="" to="" manipulate="" the="" equation="" to="" isolate="" the="" variable="" x="" on="" one="" side.="">
By subtracting 4x from both sides, we eliminate the x term on the right side and obtain 3 < x="" +="" 7.="" next,="" we="" subtract="" 7="" from="" both="" sides="" to="" isolate="" the="" x="" term="" on="" the="" right="" side,="" resulting="" in="" -4="" />< x.="" />
To express the solution in a more familiar form, we rewrite the inequality with x on the left side as x > -4. This means that x can take on any real value greater than -4.
Therefore, the correct answer is option 'C' (-4, ) which represents all real numbers greater than -4.
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The solution of inequality 4x + 3 < 5x + 7 when x is a real number isa)[4, ∞)b)(-∞, 4)c)(-4,∞)d)None of the theseCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The solution of inequality 4x + 3 < 5x + 7 when x is a real number isa)[4, ∞)b)(-∞, 4)c)(-4,∞)d)None of the theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The solution of inequality 4x + 3 < 5x + 7 when x is a real number isa)[4, ∞)b)(-∞, 4)c)(-4,∞)d)None of the theseCorrect answer is option 'C'. Can you explain this answer?.
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