Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (2x-1)& = & -5 \color{red}{-} (-12+x) \\\Leftrightarrow & 12x-6& = &-5+12-x \\\Leftrightarrow & 12x \color{red}{-6} & = &7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 12x+x& = &7+6 \\\Leftrightarrow & 13x& = &13 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{13}{ \color{red}{13} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-2x-1)& = & -15 \color{red}{+} (7+x) \\\Leftrightarrow & -8x-4& = &-15+7+x \\\Leftrightarrow & -8x \color{red}{-4} & = &-8 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -8x-x& = &-8+4 \\\Leftrightarrow & -9x& = &-4 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-4}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{4}{9} & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-6x+1)& = & 7 \color{red}{+} (-6+x) \\\Leftrightarrow & -12x+2& = &7-6+x \\\Leftrightarrow & -12x \color{red}{+2} & = &1 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & -12x-x& = &1-2 \\\Leftrightarrow & -13x& = &-1 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-1}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-5x+2)& = & 8 \color{red}{-} (2+x) \\\Leftrightarrow & -30x+12& = &8-2-x \\\Leftrightarrow & -30x \color{red}{+12} & = &6 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -30x+x& = &6-12 \\\Leftrightarrow & -29x& = &-6 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-6}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{6}{29} & & \\ & V = \left\{ \frac{6}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (4x+5)& = & -5 \color{red}{-} (-13+x) \\\Leftrightarrow & 8x+10& = &-5+13-x \\\Leftrightarrow & 8x \color{red}{+10} & = &8 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 8x+x& = &8-10 \\\Leftrightarrow & 9x& = &-2 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-2}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (3x-5)& = & -11 \color{red}{+} (-8-5x) \\\Leftrightarrow & 18x-30& = &-11-8-5x \\\Leftrightarrow & 18x \color{red}{-30} & = &-19 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-30} \color{blue}{+30} \color{blue}{+5x} & = &-19 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+30} \\\Leftrightarrow & 18x+5x& = &-19+30 \\\Leftrightarrow & 23x& = &11 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{11}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{11}{23} & & \\ & V = \left\{ \frac{11}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (4x+1)& = & 8 \color{red}{-} (13+x) \\\Leftrightarrow & 12x+3& = &8-13-x \\\Leftrightarrow & 12x \color{red}{+3} & = &-5 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 12x+x& = &-5-3 \\\Leftrightarrow & 13x& = &-8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (x-3)& = & -9 \color{red}{-} (-8+x) \\\Leftrightarrow & 4x-12& = &-9+8-x \\\Leftrightarrow & 4x \color{red}{-12} & = &-1 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 4x+x& = &-1+12 \\\Leftrightarrow & 5x& = &11 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{11}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{11}{5} & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-6x+4)& = & 12 \color{red}{-} (1-5x) \\\Leftrightarrow & -18x+12& = &12-1+5x \\\Leftrightarrow & -18x \color{red}{+12} & = &11 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -18x-5x& = &11-12 \\\Leftrightarrow & -23x& = &-1 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-1}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{1}{23} & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (2x+2)& = & 5 \color{red}{-} (-4+x) \\\Leftrightarrow & 4x+4& = &5+4-x \\\Leftrightarrow & 4x \color{red}{+4} & = &9 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 4x+x& = &9-4 \\\Leftrightarrow & 5x& = &5 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{5}{ \color{red}{5} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-x+6)& = & -8 \color{red}{-} (12+x) \\\Leftrightarrow & -4x+24& = &-8-12-x \\\Leftrightarrow & -4x \color{red}{+24} & = &-20 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -4x+x& = &-20-24 \\\Leftrightarrow & -3x& = &-44 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-44}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{44}{3} & & \\ & V = \left\{ \frac{44}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x-3)& = & -6 \color{red}{-} (7+x) \\\Leftrightarrow & 12x-18& = &-6-7-x \\\Leftrightarrow & 12x \color{red}{-18} & = &-13 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 12x+x& = &-13+18 \\\Leftrightarrow & 13x& = &5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)