Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (4x+7)& = & 13 \color{red}{-} (-14+x) \\\Leftrightarrow & 12x+21& = &13+14-x \\\Leftrightarrow & 12x \color{red}{+21} & = &27 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &27 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & 12x+x& = &27-21 \\\Leftrightarrow & 13x& = &6 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{6}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x+3)& = & 3 \color{red}{+} (-10-3x) \\\Leftrightarrow & 25x+15& = &3-10-3x \\\Leftrightarrow & 25x \color{red}{+15} & = &-7 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{+15} \color{blue}{-15} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-15} \\\Leftrightarrow & 25x+3x& = &-7-15 \\\Leftrightarrow & 28x& = &-22 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{-22}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{-11}{14} & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-x-5)& = & -3 \color{red}{-} (11-5x) \\\Leftrightarrow & -6x-30& = &-3-11+5x \\\Leftrightarrow & -6x \color{red}{-30} & = &-14 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-30} \color{blue}{+30} \color{blue}{-5x} & = &-14 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+30} \\\Leftrightarrow & -6x-5x& = &-14+30 \\\Leftrightarrow & -11x& = &16 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{16}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-16}{11} & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (x+2)& = & -2 \color{red}{-} (15+x) \\\Leftrightarrow & 4x+8& = &-2-15-x \\\Leftrightarrow & 4x \color{red}{+8} & = &-17 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 4x+x& = &-17-8 \\\Leftrightarrow & 5x& = &-25 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-25}{ \color{red}{5} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (4x-5)& = & -6 \color{red}{+} (-6+x) \\\Leftrightarrow & 8x-10& = &-6-6+x \\\Leftrightarrow & 8x \color{red}{-10} & = &-12 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 8x-x& = &-12+10 \\\Leftrightarrow & 7x& = &-2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-4x-2)& = & -8 \color{red}{-} (9+x) \\\Leftrightarrow & -20x-10& = &-8-9-x \\\Leftrightarrow & -20x \color{red}{-10} & = &-17 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -20x+x& = &-17+10 \\\Leftrightarrow & -19x& = &-7 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-7}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{7}{19} & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (4x-1)& = & 7 \color{red}{+} (8+x) \\\Leftrightarrow & 12x-3& = &7+8+x \\\Leftrightarrow & 12x \color{red}{-3} & = &15 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 12x-x& = &15+3 \\\Leftrightarrow & 11x& = &18 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{18}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{18}{11} & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (5x-4)& = & -2 \color{red}{-} (2-2x) \\\Leftrightarrow & 15x-12& = &-2-2+2x \\\Leftrightarrow & 15x \color{red}{-12} & = &-4 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-12} \color{blue}{+12} \color{blue}{-2x} & = &-4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+12} \\\Leftrightarrow & 15x-2x& = &-4+12 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (x-1)& = & 8 \color{red}{+} (3+x) \\\Leftrightarrow & 5x-5& = &8+3+x \\\Leftrightarrow & 5x \color{red}{-5} & = &11 \color{red}{+x} \\\Leftrightarrow & 5x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & 5x-x& = &11+5 \\\Leftrightarrow & 4x& = &16 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{16}{ \color{red}{4} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-3x-1)& = & -3 \color{red}{+} (9+x) \\\Leftrightarrow & -6x-2& = &-3+9+x \\\Leftrightarrow & -6x \color{red}{-2} & = &6 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -6x-x& = &6+2 \\\Leftrightarrow & -7x& = &8 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{8}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (2x-4)& = & 3 \color{red}{+} (15+3x) \\\Leftrightarrow & 8x-16& = &3+15+3x \\\Leftrightarrow & 8x \color{red}{-16} & = &18 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{-16} \color{blue}{+16} \color{blue}{-3x} & = &18 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+16} \\\Leftrightarrow & 8x-3x& = &18+16 \\\Leftrightarrow & 5x& = &34 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{34}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{34}{5} & & \\ & V = \left\{ \frac{34}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (5x-2)& = & 12 \color{red}{-} (-10+x) \\\Leftrightarrow & 30x-12& = &12+10-x \\\Leftrightarrow & 30x \color{red}{-12} & = &22 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 30x+x& = &22+12 \\\Leftrightarrow & 31x& = &34 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{34}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{34}{31} & & \\ & V = \left\{ \frac{34}{31} \right\} & \\\end{align}\)