Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(3(-2x-5)=14-(-2+x)\)
2. \(6(x-1)=3-(10-5x)\)
3. \(6(-x-2)=10-(-10-5x)\)
4. \(6(x-5)=-12-(8+x)\)
5. \(5(4x-3)=-1+(10+x)\)
6. \(5(6x-7)=9+(-15+x)\)
7. \(5(-5x-3)=2-(-4+4x)\)
8. \(5(3x+3)=15-(-2+x)\)
9. \(2(3x+3)=-1-(-6-5x)\)
10. \(2(-4x-1)=-4-(-12+x)\)
11. \(3(-6x-2)=-12-(-11-5x)\)
12. \(5(-3x+7)=1+(14+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-2x-5)& = & 14 \color{red}{-} (-2+x) \\\Leftrightarrow & -6x-15& = &14+2-x \\\Leftrightarrow & -6x \color{red}{-15} & = &16 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -6x+x& = &16+15 \\\Leftrightarrow & -5x& = &31 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{31}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-31}{5} & & \\ & V = \left\{ \frac{-31}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (x-1)& = & 3 \color{red}{-} (10-5x) \\\Leftrightarrow & 6x-6& = &3-10+5x \\\Leftrightarrow & 6x \color{red}{-6} & = &-7 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 6x-5x& = &-7+6 \\\Leftrightarrow & x& = &-1 \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-x-2)& = & 10 \color{red}{-} (-10-5x) \\\Leftrightarrow & -6x-12& = &10+10+5x \\\Leftrightarrow & -6x \color{red}{-12} & = &20 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &20 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -6x-5x& = &20+12 \\\Leftrightarrow & -11x& = &32 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{32}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-32}{11} & & \\ & V = \left\{ \frac{-32}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (x-5)& = & -12 \color{red}{-} (8+x) \\\Leftrightarrow & 6x-30& = &-12-8-x \\\Leftrightarrow & 6x \color{red}{-30} & = &-20 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 6x+x& = &-20+30 \\\Leftrightarrow & 7x& = &10 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{10}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (4x-3)& = & -1 \color{red}{+} (10+x) \\\Leftrightarrow & 20x-15& = &-1+10+x \\\Leftrightarrow & 20x \color{red}{-15} & = &9 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 20x-x& = &9+15 \\\Leftrightarrow & 19x& = &24 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{24}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{24}{19} & & \\ & V = \left\{ \frac{24}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (6x-7)& = & 9 \color{red}{+} (-15+x) \\\Leftrightarrow & 30x-35& = &9-15+x \\\Leftrightarrow & 30x \color{red}{-35} & = &-6 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & 30x-x& = &-6+35 \\\Leftrightarrow & 29x& = &29 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{29}{ \color{red}{29} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-5x-3)& = & 2 \color{red}{-} (-4+4x) \\\Leftrightarrow & -25x-15& = &2+4-4x \\\Leftrightarrow & -25x \color{red}{-15} & = &6 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &6 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & -25x+4x& = &6+15 \\\Leftrightarrow & -21x& = &21 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{21}{ \color{red}{-21} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (3x+3)& = & 15 \color{red}{-} (-2+x) \\\Leftrightarrow & 15x+15& = &15+2-x \\\Leftrightarrow & 15x \color{red}{+15} & = &17 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 15x+x& = &17-15 \\\Leftrightarrow & 16x& = &2 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{2}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{1}{8} & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (3x+3)& = & -1 \color{red}{-} (-6-5x) \\\Leftrightarrow & 6x+6& = &-1+6+5x \\\Leftrightarrow & 6x \color{red}{+6} & = &5 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 6x-5x& = &5-6 \\\Leftrightarrow & x& = &-1 \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-4x-1)& = & -4 \color{red}{-} (-12+x) \\\Leftrightarrow & -8x-2& = &-4+12-x \\\Leftrightarrow & -8x \color{red}{-2} & = &8 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -8x+x& = &8+2 \\\Leftrightarrow & -7x& = &10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-6x-2)& = & -12 \color{red}{-} (-11-5x) \\\Leftrightarrow & -18x-6& = &-12+11+5x \\\Leftrightarrow & -18x \color{red}{-6} & = &-1 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & -18x-5x& = &-1+6 \\\Leftrightarrow & -23x& = &5 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{5}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-5}{23} & & \\ & V = \left\{ \frac{-5}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-3x+7)& = & 1 \color{red}{+} (14+x) \\\Leftrightarrow & -15x+35& = &1+14+x \\\Leftrightarrow & -15x \color{red}{+35} & = &15 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -15x-x& = &15-35 \\\Leftrightarrow & -16x& = &-20 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-20}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{5}{4} & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)