Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-x+2)& = & -4 \color{red}{-} (11+x) \\\Leftrightarrow & -5x+10& = &-4-11-x \\\Leftrightarrow & -5x \color{red}{+10} & = &-15 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -5x+x& = &-15-10 \\\Leftrightarrow & -4x& = &-25 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{-25}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{25}{4} & & \\ & V = \left\{ \frac{25}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-3x-3)& = & -12 \color{red}{+} (5+x) \\\Leftrightarrow & -12x-12& = &-12+5+x \\\Leftrightarrow & -12x \color{red}{-12} & = &-7 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &-7+12 \\\Leftrightarrow & -13x& = &5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-3x+1)& = & 10 \color{red}{+} (13+x) \\\Leftrightarrow & -12x+4& = &10+13+x \\\Leftrightarrow & -12x \color{red}{+4} & = &23 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &23 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -12x-x& = &23-4 \\\Leftrightarrow & -13x& = &19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-19}{13} & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-x-2)& = & 12 \color{red}{+} (4+x) \\\Leftrightarrow & -2x-4& = &12+4+x \\\Leftrightarrow & -2x \color{red}{-4} & = &16 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -2x-x& = &16+4 \\\Leftrightarrow & -3x& = &20 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{20}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-20}{3} & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (5x+1)& = & -13 \color{red}{+} (-10-2x) \\\Leftrightarrow & 15x+3& = &-13-10-2x \\\Leftrightarrow & 15x \color{red}{+3} & = &-23 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+3} \color{blue}{-3} \color{blue}{+2x} & = &-23 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-3} \\\Leftrightarrow & 15x+2x& = &-23-3 \\\Leftrightarrow & 17x& = &-26 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-26}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-26}{17} & & \\ & V = \left\{ \frac{-26}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-5x+7)& = & 15 \color{red}{+} (7+3x) \\\Leftrightarrow & -25x+35& = &15+7+3x \\\Leftrightarrow & -25x \color{red}{+35} & = &22 \color{red}{+3x} \\\Leftrightarrow & -25x \color{red}{+35} \color{blue}{-35} \color{blue}{-3x} & = &22 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-35} \\\Leftrightarrow & -25x-3x& = &22-35 \\\Leftrightarrow & -28x& = &-13 \\\Leftrightarrow & \frac{-28x}{ \color{red}{-28} }& = &\frac{-13}{ \color{red}{-28} } \\\Leftrightarrow & x = \frac{13}{28} & & \\ & V = \left\{ \frac{13}{28} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (5x-2)& = & 11 \color{red}{-} (-4+x) \\\Leftrightarrow & 30x-12& = &11+4-x \\\Leftrightarrow & 30x \color{red}{-12} & = &15 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 30x+x& = &15+12 \\\Leftrightarrow & 31x& = &27 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{27}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{27}{31} & & \\ & V = \left\{ \frac{27}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-3x+3)& = & 3 \color{red}{-} (1+x) \\\Leftrightarrow & -18x+18& = &3-1-x \\\Leftrightarrow & -18x \color{red}{+18} & = &2 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -18x+x& = &2-18 \\\Leftrightarrow & -17x& = &-16 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-16}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{16}{17} & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-2x+7)& = & -13 \color{red}{+} (-5+x) \\\Leftrightarrow & -12x+42& = &-13-5+x \\\Leftrightarrow & -12x \color{red}{+42} & = &-18 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -12x-x& = &-18-42 \\\Leftrightarrow & -13x& = &-60 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-60}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{60}{13} & & \\ & V = \left\{ \frac{60}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (2x+2)& = & 5 \color{red}{+} (-12-5x) \\\Leftrightarrow & 6x+6& = &5-12-5x \\\Leftrightarrow & 6x \color{red}{+6} & = &-7 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &-7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 6x+5x& = &-7-6 \\\Leftrightarrow & 11x& = &-13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (x-2)& = & 8 \color{red}{-} (2+x) \\\Leftrightarrow & 2x-4& = &8-2-x \\\Leftrightarrow & 2x \color{red}{-4} & = &6 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 2x+x& = &6+4 \\\Leftrightarrow & 3x& = &10 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{10}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{10}{3} & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-6x+1)& = & 13 \color{red}{-} (4-5x) \\\Leftrightarrow & -18x+3& = &13-4+5x \\\Leftrightarrow & -18x \color{red}{+3} & = &9 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+3} \color{blue}{-3} \color{blue}{-5x} & = &9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-3} \\\Leftrightarrow & -18x-5x& = &9-3 \\\Leftrightarrow & -23x& = &6 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{6}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-6}{23} & & \\ & V = \left\{ \frac{-6}{23} \right\} & \\\end{align}\)