Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (4x-5)& = & -8 \color{red}{-} (3-3x) \\\Leftrightarrow & 16x-20& = &-8-3+3x \\\Leftrightarrow & 16x \color{red}{-20} & = &-11 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &-11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & 16x-3x& = &-11+20 \\\Leftrightarrow & 13x& = &9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (2x+1)& = & -13 \color{red}{-} (6+x) \\\Leftrightarrow & 8x+4& = &-13-6-x \\\Leftrightarrow & 8x \color{red}{+4} & = &-19 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 8x+x& = &-19-4 \\\Leftrightarrow & 9x& = &-23 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-23}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-23}{9} & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (5x-7)& = & -6 \color{red}{-} (-6+x) \\\Leftrightarrow & 10x-14& = &-6+6-x \\\Leftrightarrow & 10x \color{red}{-14} & = &0 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 10x+x& = &0+14 \\\Leftrightarrow & 11x& = &14 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{14}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{14}{11} & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (x-6)& = & -5 \color{red}{-} (1+3x) \\\Leftrightarrow & 4x-24& = &-5-1-3x \\\Leftrightarrow & 4x \color{red}{-24} & = &-6 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &-6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & 4x+3x& = &-6+24 \\\Leftrightarrow & 7x& = &18 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{18}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{18}{7} & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-5x+2)& = & 6 \color{red}{+} (-6+3x) \\\Leftrightarrow & -20x+8& = &6-6+3x \\\Leftrightarrow & -20x \color{red}{+8} & = &0 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -20x-3x& = &0-8 \\\Leftrightarrow & -23x& = &-8 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-8}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{8}{23} & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-3x-1)& = & 12 \color{red}{-} (7+x) \\\Leftrightarrow & -6x-2& = &12-7-x \\\Leftrightarrow & -6x \color{red}{-2} & = &5 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -6x+x& = &5+2 \\\Leftrightarrow & -5x& = &7 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{7}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-7}{5} & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-2x+7)& = & 2 \color{red}{+} (8-3x) \\\Leftrightarrow & -10x+35& = &2+8-3x \\\Leftrightarrow & -10x \color{red}{+35} & = &10 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+35} \color{blue}{-35} \color{blue}{+3x} & = &10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-35} \\\Leftrightarrow & -10x+3x& = &10-35 \\\Leftrightarrow & -7x& = &-25 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-25}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{25}{7} & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x+1)& = & 10 \color{red}{+} (8+x) \\\Leftrightarrow & -8x+2& = &10+8+x \\\Leftrightarrow & -8x \color{red}{+2} & = &18 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & -8x-x& = &18-2 \\\Leftrightarrow & -9x& = &16 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{16}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-16}{9} & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (6x-1)& = & -11 \color{red}{-} (9+x) \\\Leftrightarrow & 18x-3& = &-11-9-x \\\Leftrightarrow & 18x \color{red}{-3} & = &-20 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 18x+x& = &-20+3 \\\Leftrightarrow & 19x& = &-17 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-17}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-17}{19} & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-3x+1)& = & 9 \color{red}{+} (-8-2x) \\\Leftrightarrow & -15x+5& = &9-8-2x \\\Leftrightarrow & -15x \color{red}{+5} & = &1 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+5} \color{blue}{-5} \color{blue}{+2x} & = &1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-5} \\\Leftrightarrow & -15x+2x& = &1-5 \\\Leftrightarrow & -13x& = &-4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (5x+7)& = & -13 \color{red}{+} (15+x) \\\Leftrightarrow & 15x+21& = &-13+15+x \\\Leftrightarrow & 15x \color{red}{+21} & = &2 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & 15x-x& = &2-21 \\\Leftrightarrow & 14x& = &-19 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-19}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-19}{14} & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x-6)& = & -6 \color{red}{-} (7+x) \\\Leftrightarrow & -30x-30& = &-6-7-x \\\Leftrightarrow & -30x \color{red}{-30} & = &-13 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -30x+x& = &-13+30 \\\Leftrightarrow & -29x& = &17 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{17}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-17}{29} & & \\ & V = \left\{ \frac{-17}{29} \right\} & \\\end{align}\)