Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (3x+7)& = & 13 \color{red}{-} (7+2x) \\\Leftrightarrow & 9x+21& = &13-7-2x \\\Leftrightarrow & 9x \color{red}{+21} & = &6 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+21} \color{blue}{-21} \color{blue}{+2x} & = &6 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-21} \\\Leftrightarrow & 9x+2x& = &6-21 \\\Leftrightarrow & 11x& = &-15 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-15}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-15}{11} & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-5x+1)& = & 14 \color{red}{-} (11-4x) \\\Leftrightarrow & -25x+5& = &14-11+4x \\\Leftrightarrow & -25x \color{red}{+5} & = &3 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{+5} \color{blue}{-5} \color{blue}{-4x} & = &3 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-5} \\\Leftrightarrow & -25x-4x& = &3-5 \\\Leftrightarrow & -29x& = &-2 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-2}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{2}{29} & & \\ & V = \left\{ \frac{2}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (x-2)& = & 15 \color{red}{+} (3+2x) \\\Leftrightarrow & 3x-6& = &15+3+2x \\\Leftrightarrow & 3x \color{red}{-6} & = &18 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{-6} \color{blue}{+6} \color{blue}{-2x} & = &18 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+6} \\\Leftrightarrow & 3x-2x& = &18+6 \\\Leftrightarrow & x& = &24 \\ & V = \left\{ 24 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-5x+6)& = & -15 \color{red}{-} (-13-3x) \\\Leftrightarrow & -10x+12& = &-15+13+3x \\\Leftrightarrow & -10x \color{red}{+12} & = &-2 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & -10x-3x& = &-2-12 \\\Leftrightarrow & -13x& = &-14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (4x+3)& = & -8 \color{red}{-} (-13+x) \\\Leftrightarrow & 12x+9& = &-8+13-x \\\Leftrightarrow & 12x \color{red}{+9} & = &5 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & 12x+x& = &5-9 \\\Leftrightarrow & 13x& = &-4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (5x-7)& = & 12 \color{red}{+} (6+x) \\\Leftrightarrow & 15x-21& = &12+6+x \\\Leftrightarrow & 15x \color{red}{-21} & = &18 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 15x-x& = &18+21 \\\Leftrightarrow & 14x& = &39 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{39}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{39}{14} & & \\ & V = \left\{ \frac{39}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (2x+2)& = & 11 \color{red}{+} (-4+x) \\\Leftrightarrow & 12x+12& = &11-4+x \\\Leftrightarrow & 12x \color{red}{+12} & = &7 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &7-12 \\\Leftrightarrow & 11x& = &-5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-3x+1)& = & -6 \color{red}{+} (-7+x) \\\Leftrightarrow & -6x+2& = &-6-7+x \\\Leftrightarrow & -6x \color{red}{+2} & = &-13 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & -6x-x& = &-13-2 \\\Leftrightarrow & -7x& = &-15 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-15}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{15}{7} & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (4x+7)& = & -5 \color{red}{-} (13-5x) \\\Leftrightarrow & 16x+28& = &-5-13+5x \\\Leftrightarrow & 16x \color{red}{+28} & = &-18 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{+28} \color{blue}{-28} \color{blue}{-5x} & = &-18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-28} \\\Leftrightarrow & 16x-5x& = &-18-28 \\\Leftrightarrow & 11x& = &-46 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-46}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-46}{11} & & \\ & V = \left\{ \frac{-46}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (x-2)& = & 15 \color{red}{+} (-5+x) \\\Leftrightarrow & 2x-4& = &15-5+x \\\Leftrightarrow & 2x \color{red}{-4} & = &10 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 2x-x& = &10+4 \\\Leftrightarrow & x& = &14 \\ & V = \left\{ 14 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-4x+1)& = & -9 \color{red}{-} (9+x) \\\Leftrightarrow & -24x+6& = &-9-9-x \\\Leftrightarrow & -24x \color{red}{+6} & = &-18 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -24x+x& = &-18-6 \\\Leftrightarrow & -23x& = &-24 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-24}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{24}{23} & & \\ & V = \left\{ \frac{24}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x-6)& = & -10 \color{red}{-} (-7+x) \\\Leftrightarrow & 30x-30& = &-10+7-x \\\Leftrightarrow & 30x \color{red}{-30} & = &-3 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 30x+x& = &-3+30 \\\Leftrightarrow & 31x& = &27 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{27}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{27}{31} & & \\ & V = \left\{ \frac{27}{31} \right\} & \\\end{align}\)