Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (x+6)& = & -10 \color{red}{+} (12+3x) \\\Leftrightarrow & 4x+24& = &-10+12+3x \\\Leftrightarrow & 4x \color{red}{+24} & = &2 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+24} \color{blue}{-24} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-24} \\\Leftrightarrow & 4x-3x& = &2-24 \\\Leftrightarrow & x& = &-22 \\ & V = \left\{ -22 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (5x-7)& = & 14 \color{red}{+} (-10+x) \\\Leftrightarrow & 30x-42& = &14-10+x \\\Leftrightarrow & 30x \color{red}{-42} & = &4 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 30x-x& = &4+42 \\\Leftrightarrow & 29x& = &46 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{46}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{46}{29} & & \\ & V = \left\{ \frac{46}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-5x-5)& = & -4 \color{red}{+} (-1+x) \\\Leftrightarrow & -20x-20& = &-4-1+x \\\Leftrightarrow & -20x \color{red}{-20} & = &-5 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -20x-x& = &-5+20 \\\Leftrightarrow & -21x& = &15 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{15}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (6x+7)& = & 2 \color{red}{+} (1+x) \\\Leftrightarrow & 30x+35& = &2+1+x \\\Leftrightarrow & 30x \color{red}{+35} & = &3 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & 30x-x& = &3-35 \\\Leftrightarrow & 29x& = &-32 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-32}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-32}{29} & & \\ & V = \left\{ \frac{-32}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-2x+2)& = & 4 \color{red}{+} (-1+x) \\\Leftrightarrow & -10x+10& = &4-1+x \\\Leftrightarrow & -10x \color{red}{+10} & = &3 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -10x-x& = &3-10 \\\Leftrightarrow & -11x& = &-7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (2x+7)& = & 8 \color{red}{+} (-15-5x) \\\Leftrightarrow & 6x+21& = &8-15-5x \\\Leftrightarrow & 6x \color{red}{+21} & = &-7 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+21} \color{blue}{-21} \color{blue}{+5x} & = &-7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-21} \\\Leftrightarrow & 6x+5x& = &-7-21 \\\Leftrightarrow & 11x& = &-28 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-28}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-28}{11} & & \\ & V = \left\{ \frac{-28}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (5x+1)& = & -11 \color{red}{+} (7-4x) \\\Leftrightarrow & 25x+5& = &-11+7-4x \\\Leftrightarrow & 25x \color{red}{+5} & = &-4 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{+5} \color{blue}{-5} \color{blue}{+4x} & = &-4 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-5} \\\Leftrightarrow & 25x+4x& = &-4-5 \\\Leftrightarrow & 29x& = &-9 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-9}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-9}{29} & & \\ & V = \left\{ \frac{-9}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x-7)& = & -8 \color{red}{-} (2+x) \\\Leftrightarrow & 24x-42& = &-8-2-x \\\Leftrightarrow & 24x \color{red}{-42} & = &-10 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 24x+x& = &-10+42 \\\Leftrightarrow & 25x& = &32 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{32}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{32}{25} & & \\ & V = \left\{ \frac{32}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-x-7)& = & 4 \color{red}{+} (2+4x) \\\Leftrightarrow & -3x-21& = &4+2+4x \\\Leftrightarrow & -3x \color{red}{-21} & = &6 \color{red}{+4x} \\\Leftrightarrow & -3x \color{red}{-21} \color{blue}{+21} \color{blue}{-4x} & = &6 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+21} \\\Leftrightarrow & -3x-4x& = &6+21 \\\Leftrightarrow & -7x& = &27 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{27}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-27}{7} & & \\ & V = \left\{ \frac{-27}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-x-1)& = & -6 \color{red}{-} (9+x) \\\Leftrightarrow & -5x-5& = &-6-9-x \\\Leftrightarrow & -5x \color{red}{-5} & = &-15 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & -5x+x& = &-15+5 \\\Leftrightarrow & -4x& = &-10 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{-10}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{5}{2} & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (5x+7)& = & -12 \color{red}{-} (-13+3x) \\\Leftrightarrow & 25x+35& = &-12+13-3x \\\Leftrightarrow & 25x \color{red}{+35} & = &1 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{+35} \color{blue}{-35} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-35} \\\Leftrightarrow & 25x+3x& = &1-35 \\\Leftrightarrow & 28x& = &-34 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{-34}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{-17}{14} & & \\ & V = \left\{ \frac{-17}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-4x+6)& = & 3 \color{red}{-} (6+x) \\\Leftrightarrow & -24x+36& = &3-6-x \\\Leftrightarrow & -24x \color{red}{+36} & = &-3 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -24x+x& = &-3-36 \\\Leftrightarrow & -23x& = &-39 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-39}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{39}{23} & & \\ & V = \left\{ \frac{39}{23} \right\} & \\\end{align}\)