Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(2(3x-2)=4-(-15-5x)\)
2. \(2(-x-4)=-3-(-1+x)\)
3. \(4(-6x-4)=6-(-5+x)\)
4. \(5(-6x+4)=-13-(-3+x)\)
5. \(2(2x+1)=-11+(13+x)\)
6. \(4(-3x+1)=-9-(-10+x)\)
7. \(6(x-5)=-12+(9+x)\)
8. \(3(-5x+2)=-5+(-12+x)\)
9. \(2(-5x+2)=4+(-8-3x)\)
10. \(2(4x-7)=5-(-12+3x)\)
11. \(2(-3x+5)=8+(8-5x)\)
12. \(2(-5x-3)=6-(1-3x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (3x-2)& = & 4 \color{red}{-} (-15-5x) \\\Leftrightarrow & 6x-4& = &4+15+5x \\\Leftrightarrow & 6x \color{red}{-4} & = &19 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-4} \color{blue}{+4} \color{blue}{-5x} & = &19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+4} \\\Leftrightarrow & 6x-5x& = &19+4 \\\Leftrightarrow & x& = &23 \\ & V = \left\{ 23 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-x-4)& = & -3 \color{red}{-} (-1+x) \\\Leftrightarrow & -2x-8& = &-3+1-x \\\Leftrightarrow & -2x \color{red}{-8} & = &-2 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -2x+x& = &-2+8 \\\Leftrightarrow & -x& = &6 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{6}{ \color{red}{-1} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-6x-4)& = & 6 \color{red}{-} (-5+x) \\\Leftrightarrow & -24x-16& = &6+5-x \\\Leftrightarrow & -24x \color{red}{-16} & = &11 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -24x+x& = &11+16 \\\Leftrightarrow & -23x& = &27 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{27}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-27}{23} & & \\ & V = \left\{ \frac{-27}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-6x+4)& = & -13 \color{red}{-} (-3+x) \\\Leftrightarrow & -30x+20& = &-13+3-x \\\Leftrightarrow & -30x \color{red}{+20} & = &-10 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -30x+x& = &-10-20 \\\Leftrightarrow & -29x& = &-30 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-30}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{30}{29} & & \\ & V = \left\{ \frac{30}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (2x+1)& = & -11 \color{red}{+} (13+x) \\\Leftrightarrow & 4x+2& = &-11+13+x \\\Leftrightarrow & 4x \color{red}{+2} & = &2 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & 4x-x& = &2-2 \\\Leftrightarrow & 3x& = &0 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{0}{ \color{red}{3} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-3x+1)& = & -9 \color{red}{-} (-10+x) \\\Leftrightarrow & -12x+4& = &-9+10-x \\\Leftrightarrow & -12x \color{red}{+4} & = &1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -12x+x& = &1-4 \\\Leftrightarrow & -11x& = &-3 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-3}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (x-5)& = & -12 \color{red}{+} (9+x) \\\Leftrightarrow & 6x-30& = &-12+9+x \\\Leftrightarrow & 6x \color{red}{-30} & = &-3 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 6x-x& = &-3+30 \\\Leftrightarrow & 5x& = &27 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{27}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{27}{5} & & \\ & V = \left\{ \frac{27}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x+2)& = & -5 \color{red}{+} (-12+x) \\\Leftrightarrow & -15x+6& = &-5-12+x \\\Leftrightarrow & -15x \color{red}{+6} & = &-17 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -15x-x& = &-17-6 \\\Leftrightarrow & -16x& = &-23 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-23}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{23}{16} & & \\ & V = \left\{ \frac{23}{16} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-5x+2)& = & 4 \color{red}{+} (-8-3x) \\\Leftrightarrow & -10x+4& = &4-8-3x \\\Leftrightarrow & -10x \color{red}{+4} & = &-4 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & -10x+3x& = &-4-4 \\\Leftrightarrow & -7x& = &-8 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-8}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (4x-7)& = & 5 \color{red}{-} (-12+3x) \\\Leftrightarrow & 8x-14& = &5+12-3x \\\Leftrightarrow & 8x \color{red}{-14} & = &17 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & 8x+3x& = &17+14 \\\Leftrightarrow & 11x& = &31 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{31}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{31}{11} & & \\ & V = \left\{ \frac{31}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-3x+5)& = & 8 \color{red}{+} (8-5x) \\\Leftrightarrow & -6x+10& = &8+8-5x \\\Leftrightarrow & -6x \color{red}{+10} & = &16 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+10} \color{blue}{-10} \color{blue}{+5x} & = &16 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-10} \\\Leftrightarrow & -6x+5x& = &16-10 \\\Leftrightarrow & -x& = &6 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{6}{ \color{red}{-1} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-5x-3)& = & 6 \color{red}{-} (1-3x) \\\Leftrightarrow & -10x-6& = &6-1+3x \\\Leftrightarrow & -10x \color{red}{-6} & = &5 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-6} \color{blue}{+6} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+6} \\\Leftrightarrow & -10x-3x& = &5+6 \\\Leftrightarrow & -13x& = &11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-11}{13} & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)