4(x-5)=4x-5 find and correct the errors in the following mathematical statements. step by step explanation
Answers
Find and correct the errors in the following mathematical statements.
a) 4(x-5)=4x-5
b) x\left(3x+2\right)=3x^2+2x(3x+2)=3x
2
+2
c) 2x+3y=5xy2x+3y=5xy
d) x+2x+3x=5xx+2x+3x=5x
e) 5y+2y+y-7y=05y+2y+y−7y=0
f) 3x+2x=5x^23x+2x=5x
2
g) \left(2x\right)^2+4\left(2x\right)+7=2x^2=8x+7(2x)
2
+4(2x)+7=2x
2
=8x+7
h) \left(2x\right)^2+5x=4x+5x=9x(2x)
2
+5x=4x+5x=9x
i) \left(3x+2\right)^2+3x^2+6x+4(3x+2)
2
+3x
2
+6x+4
Solution 1:
a) 4(x-5)=4x-5
Correction=
4\left(x-5\right)\ne4x-54(x−5)
=4x−5
4\left(x-5\right)=\ 4x-204(x−5)= 4x−20
b) x\left(3x+2\right)=3x^2+2x(3x+2)=3x
2
+2
Correction= x\left(3x+2\right)\ne3x^2+3yx(3x+2)
=3x
2
+3y
x\left(3x+2\right)=3^2+2xx(3x+2)=3
2
+2x
c) 2x+3y=5xy2x+3y=5xy
Correction= x\left(3x+2\right)\ne3x^2+2xx(3x+2)
=3x
2
+2x
2x+3y=2x+3y
d) x+2x+3x=5xx+2x+3x=5x
Correction= x+2x+3x\ne5xx+2x+3x
=5x
x+2x+3x=6xx+2x+3x=6x
e) 5y+2y+y-7y=05y+2y+y−7y=0
Correction= 5y+2y+y-7y\ne05y+2y+y−7y
=0
5y+2y+y-7y=8y-7y5y+2y+y−7y=8y−7y
f) 3x+2x=5x^23x+2x=5x
2
Correction=
3x+2x\ne5x^23x+2x
=5x
2
3x+2x=5x3x+2x=5x
g) \left(2x\right)^2+4\left(2x\right)+7=2x^2=8x+7(2x)
2
+4(2x)+7=2x
2
=8x+7
Correction= \left(2x\right)^2+4\left(2x\right)+7=2x^2+8x+7(2x)
2
+4(2x)+7=2x
2
+8x+7
\left(2x\right)^2+4\left(2x\right)+7=4x^2+8x+7(2x)
2
+4(2x)+7=4x
2
+8x+7
h) \left(2x\right)^2+5x=4x+5x=9x(2x)
2
+5x=4x+5x=9x
Correction= 2x^2+5x\ne4x+5x2x
2
+5x
=4x+5x
\left(2x\right)^2+5x=4x^2+5x(2x)
2
+5x=4x
2
+5x
i) \left(3x+2\right)^2+3x^2+6x+4(3x+2)
2
+3x
2
+6x+4
Correction: \left(3x+2\right)^2+3x^2+6x+4(3x+2)
2
+3x
2
+6x+4
\left(3x+2\right)^2+9x^2+12x+4(3x+2)
2
+9x
2
+12x+4