Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-5x+6)& = & -12 \color{red}{-} (12-2x) \\\Leftrightarrow & -25x+30& = &-12-12+2x \\\Leftrightarrow & -25x \color{red}{+30} & = &-24 \color{red}{+2x} \\\Leftrightarrow & -25x \color{red}{+30} \color{blue}{-30} \color{blue}{-2x} & = &-24 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-30} \\\Leftrightarrow & -25x-2x& = &-24-30 \\\Leftrightarrow & -27x& = &-54 \\\Leftrightarrow & \frac{-27x}{ \color{red}{-27} }& = &\frac{-54}{ \color{red}{-27} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-6x+7)& = & 6 \color{red}{+} (15+x) \\\Leftrightarrow & -30x+35& = &6+15+x \\\Leftrightarrow & -30x \color{red}{+35} & = &21 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -30x-x& = &21-35 \\\Leftrightarrow & -31x& = &-14 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-14}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{14}{31} & & \\ & V = \left\{ \frac{14}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (4x+3)& = & -3 \color{red}{+} (11+x) \\\Leftrightarrow & 8x+6& = &-3+11+x \\\Leftrightarrow & 8x \color{red}{+6} & = &8 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 8x-x& = &8-6 \\\Leftrightarrow & 7x& = &2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-4x+5)& = & 9 \color{red}{-} (-5+3x) \\\Leftrightarrow & -20x+25& = &9+5-3x \\\Leftrightarrow & -20x \color{red}{+25} & = &14 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{+25} \color{blue}{-25} \color{blue}{+3x} & = &14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-25} \\\Leftrightarrow & -20x+3x& = &14-25 \\\Leftrightarrow & -17x& = &-11 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-11}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{11}{17} & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x-6)& = & 7 \color{red}{-} (13+x) \\\Leftrightarrow & -30x-30& = &7-13-x \\\Leftrightarrow & -30x \color{red}{-30} & = &-6 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -30x+x& = &-6+30 \\\Leftrightarrow & -29x& = &24 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{24}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-24}{29} & & \\ & V = \left\{ \frac{-24}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-3x-2)& = & -10 \color{red}{+} (-6+x) \\\Leftrightarrow & -12x-8& = &-10-6+x \\\Leftrightarrow & -12x \color{red}{-8} & = &-16 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -12x-x& = &-16+8 \\\Leftrightarrow & -13x& = &-8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-4x+6)& = & 9 \color{red}{+} (12+x) \\\Leftrightarrow & -24x+36& = &9+12+x \\\Leftrightarrow & -24x \color{red}{+36} & = &21 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -24x-x& = &21-36 \\\Leftrightarrow & -25x& = &-15 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-15}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{3}{5} & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-3x+2)& = & -3 \color{red}{-} (-4-5x) \\\Leftrightarrow & -6x+4& = &-3+4+5x \\\Leftrightarrow & -6x \color{red}{+4} & = &1 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+4} \color{blue}{-4} \color{blue}{-5x} & = &1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-4} \\\Leftrightarrow & -6x-5x& = &1-4 \\\Leftrightarrow & -11x& = &-3 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-3}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x+7)& = & -2 \color{red}{-} (12+x) \\\Leftrightarrow & 24x+42& = &-2-12-x \\\Leftrightarrow & 24x \color{red}{+42} & = &-14 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 24x+x& = &-14-42 \\\Leftrightarrow & 25x& = &-56 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-56}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-56}{25} & & \\ & V = \left\{ \frac{-56}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (3x-4)& = & 9 \color{red}{-} (2+x) \\\Leftrightarrow & 12x-16& = &9-2-x \\\Leftrightarrow & 12x \color{red}{-16} & = &7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 12x+x& = &7+16 \\\Leftrightarrow & 13x& = &23 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{23}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{23}{13} & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (3x+6)& = & 5 \color{red}{+} (6+4x) \\\Leftrightarrow & 9x+18& = &5+6+4x \\\Leftrightarrow & 9x \color{red}{+18} & = &11 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{+18} \color{blue}{-18} \color{blue}{-4x} & = &11 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-18} \\\Leftrightarrow & 9x-4x& = &11-18 \\\Leftrightarrow & 5x& = &-7 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-7}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-7}{5} & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-5x-3)& = & -10 \color{red}{-} (13+x) \\\Leftrightarrow & -30x-18& = &-10-13-x \\\Leftrightarrow & -30x \color{red}{-18} & = &-23 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -30x+x& = &-23+18 \\\Leftrightarrow & -29x& = &-5 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-5}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{5}{29} & & \\ & V = \left\{ \frac{5}{29} \right\} & \\\end{align}\)