Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (2x+4)& = & -3 \color{red}{-} (-9-3x) \\\Leftrightarrow & 4x+8& = &-3+9+3x \\\Leftrightarrow & 4x \color{red}{+8} & = &6 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & 4x-3x& = &6-8 \\\Leftrightarrow & x& = &-2 \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (3x+2)& = & 2 \color{red}{+} (11+x) \\\Leftrightarrow & 15x+10& = &2+11+x \\\Leftrightarrow & 15x \color{red}{+10} & = &13 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 15x-x& = &13-10 \\\Leftrightarrow & 14x& = &3 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{3}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{3}{14} & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x-7)& = & 15 \color{red}{+} (14-2x) \\\Leftrightarrow & 15x-35& = &15+14-2x \\\Leftrightarrow & 15x \color{red}{-35} & = &29 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-35} \color{blue}{+35} \color{blue}{+2x} & = &29 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+35} \\\Leftrightarrow & 15x+2x& = &29+35 \\\Leftrightarrow & 17x& = &64 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{64}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{64}{17} & & \\ & V = \left\{ \frac{64}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (6x+4)& = & -1 \color{red}{+} (2-5x) \\\Leftrightarrow & 36x+24& = &-1+2-5x \\\Leftrightarrow & 36x \color{red}{+24} & = &1 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & 36x+5x& = &1-24 \\\Leftrightarrow & 41x& = &-23 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{-23}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{-23}{41} & & \\ & V = \left\{ \frac{-23}{41} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x-7)& = & -11 \color{red}{+} (-6-5x) \\\Leftrightarrow & 36x-42& = &-11-6-5x \\\Leftrightarrow & 36x \color{red}{-42} & = &-17 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{-42} \color{blue}{+42} \color{blue}{+5x} & = &-17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+42} \\\Leftrightarrow & 36x+5x& = &-17+42 \\\Leftrightarrow & 41x& = &25 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{25}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{25}{41} & & \\ & V = \left\{ \frac{25}{41} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (5x+4)& = & -14 \color{red}{+} (-11+x) \\\Leftrightarrow & 30x+24& = &-14-11+x \\\Leftrightarrow & 30x \color{red}{+24} & = &-25 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 30x-x& = &-25-24 \\\Leftrightarrow & 29x& = &-49 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-49}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-49}{29} & & \\ & V = \left\{ \frac{-49}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-5x-2)& = & -15 \color{red}{+} (2-2x) \\\Leftrightarrow & -15x-6& = &-15+2-2x \\\Leftrightarrow & -15x \color{red}{-6} & = &-13 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-6} \color{blue}{+6} \color{blue}{+2x} & = &-13 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+6} \\\Leftrightarrow & -15x+2x& = &-13+6 \\\Leftrightarrow & -13x& = &-7 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-7}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (3x+1)& = & 15 \color{red}{-} (9-2x) \\\Leftrightarrow & 15x+5& = &15-9+2x \\\Leftrightarrow & 15x \color{red}{+5} & = &6 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &6 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & 15x-2x& = &6-5 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (6x-1)& = & 14 \color{red}{-} (-13-5x) \\\Leftrightarrow & 18x-3& = &14+13+5x \\\Leftrightarrow & 18x \color{red}{-3} & = &27 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &27 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & 18x-5x& = &27+3 \\\Leftrightarrow & 13x& = &30 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{30}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{30}{13} & & \\ & V = \left\{ \frac{30}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (5x-2)& = & 12 \color{red}{-} (1+x) \\\Leftrightarrow & 15x-6& = &12-1-x \\\Leftrightarrow & 15x \color{red}{-6} & = &11 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 15x+x& = &11+6 \\\Leftrightarrow & 16x& = &17 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{17}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{17}{16} & & \\ & V = \left\{ \frac{17}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (6x+6)& = & -2 \color{red}{-} (8+x) \\\Leftrightarrow & 24x+24& = &-2-8-x \\\Leftrightarrow & 24x \color{red}{+24} & = &-10 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &-10-24 \\\Leftrightarrow & 25x& = &-34 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-34}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-34}{25} & & \\ & V = \left\{ \frac{-34}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (6x+1)& = & -7 \color{red}{+} (15+x) \\\Leftrightarrow & 18x+3& = &-7+15+x \\\Leftrightarrow & 18x \color{red}{+3} & = &8 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 18x-x& = &8-3 \\\Leftrightarrow & 17x& = &5 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{5}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{5}{17} & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)