Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(4(6x+3)=2-(15+x)\)
2. \(2(-6x+5)=-9-(13+x)\)
3. \(4(x-4)=-10+(10-3x)\)
4. \(5(6x+5)=5-(-15+x)\)
5. \(5(5x+1)=7+(-12+x)\)
6. \(5(3x-1)=3-(15+x)\)
7. \(2(-2x+7)=-4-(1+x)\)
8. \(3(-5x-4)=10+(5+x)\)
9. \(5(5x-6)=1-(-8-3x)\)
10. \(5(2x-4)=14+(1+3x)\)
11. \(4(x+5)=14+(14+x)\)
12. \(2(3x-3)=-2-(-4-5x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (6x+3)& = & 2 \color{red}{-} (15+x) \\\Leftrightarrow & 24x+12& = &2-15-x \\\Leftrightarrow & 24x \color{red}{+12} & = &-13 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 24x+x& = &-13-12 \\\Leftrightarrow & 25x& = &-25 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-25}{ \color{red}{25} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-6x+5)& = & -9 \color{red}{-} (13+x) \\\Leftrightarrow & -12x+10& = &-9-13-x \\\Leftrightarrow & -12x \color{red}{+10} & = &-22 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -12x+x& = &-22-10 \\\Leftrightarrow & -11x& = &-32 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-32}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{32}{11} & & \\ & V = \left\{ \frac{32}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (x-4)& = & -10 \color{red}{+} (10-3x) \\\Leftrightarrow & 4x-16& = &-10+10-3x \\\Leftrightarrow & 4x \color{red}{-16} & = &0 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &0 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & 4x+3x& = &0+16 \\\Leftrightarrow & 7x& = &16 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{16}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (6x+5)& = & 5 \color{red}{-} (-15+x) \\\Leftrightarrow & 30x+25& = &5+15-x \\\Leftrightarrow & 30x \color{red}{+25} & = &20 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & 30x+x& = &20-25 \\\Leftrightarrow & 31x& = &-5 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-5}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-5}{31} & & \\ & V = \left\{ \frac{-5}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (5x+1)& = & 7 \color{red}{+} (-12+x) \\\Leftrightarrow & 25x+5& = &7-12+x \\\Leftrightarrow & 25x \color{red}{+5} & = &-5 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & 25x-x& = &-5-5 \\\Leftrightarrow & 24x& = &-10 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{-10}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{-5}{12} & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (3x-1)& = & 3 \color{red}{-} (15+x) \\\Leftrightarrow & 15x-5& = &3-15-x \\\Leftrightarrow & 15x \color{red}{-5} & = &-12 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & 15x+x& = &-12+5 \\\Leftrightarrow & 16x& = &-7 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{-7}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{-7}{16} & & \\ & V = \left\{ \frac{-7}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-2x+7)& = & -4 \color{red}{-} (1+x) \\\Leftrightarrow & -4x+14& = &-4-1-x \\\Leftrightarrow & -4x \color{red}{+14} & = &-5 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -4x+x& = &-5-14 \\\Leftrightarrow & -3x& = &-19 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-19}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{19}{3} & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x-4)& = & 10 \color{red}{+} (5+x) \\\Leftrightarrow & -15x-12& = &10+5+x \\\Leftrightarrow & -15x \color{red}{-12} & = &15 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -15x-x& = &15+12 \\\Leftrightarrow & -16x& = &27 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{27}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{-27}{16} & & \\ & V = \left\{ \frac{-27}{16} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (5x-6)& = & 1 \color{red}{-} (-8-3x) \\\Leftrightarrow & 25x-30& = &1+8+3x \\\Leftrightarrow & 25x \color{red}{-30} & = &9 \color{red}{+3x} \\\Leftrightarrow & 25x \color{red}{-30} \color{blue}{+30} \color{blue}{-3x} & = &9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+30} \\\Leftrightarrow & 25x-3x& = &9+30 \\\Leftrightarrow & 22x& = &39 \\\Leftrightarrow & \frac{22x}{ \color{red}{22} }& = &\frac{39}{ \color{red}{22} } \\\Leftrightarrow & x = \frac{39}{22} & & \\ & V = \left\{ \frac{39}{22} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x-4)& = & 14 \color{red}{+} (1+3x) \\\Leftrightarrow & 10x-20& = &14+1+3x \\\Leftrightarrow & 10x \color{red}{-20} & = &15 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & 10x-3x& = &15+20 \\\Leftrightarrow & 7x& = &35 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{35}{ \color{red}{7} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (x+5)& = & 14 \color{red}{+} (14+x) \\\Leftrightarrow & 4x+20& = &14+14+x \\\Leftrightarrow & 4x \color{red}{+20} & = &28 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &28 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 4x-x& = &28-20 \\\Leftrightarrow & 3x& = &8 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{8}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{8}{3} & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (3x-3)& = & -2 \color{red}{-} (-4-5x) \\\Leftrightarrow & 6x-6& = &-2+4+5x \\\Leftrightarrow & 6x \color{red}{-6} & = &2 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 6x-5x& = &2+6 \\\Leftrightarrow & x& = &8 \\ & V = \left\{ 8 \right\} & \\\end{align}\)