Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (5x+2)& = & -2 \color{red}{-} (11+x) \\\Leftrightarrow & 15x+6& = &-2-11-x \\\Leftrightarrow & 15x \color{red}{+6} & = &-13 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 15x+x& = &-13-6 \\\Leftrightarrow & 16x& = &-19 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{-19}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{-19}{16} & & \\ & V = \left\{ \frac{-19}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-6x-6)& = & 13 \color{red}{-} (-8+x) \\\Leftrightarrow & -24x-24& = &13+8-x \\\Leftrightarrow & -24x \color{red}{-24} & = &21 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -24x+x& = &21+24 \\\Leftrightarrow & -23x& = &45 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{45}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-45}{23} & & \\ & V = \left\{ \frac{-45}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (4x+6)& = & -7 \color{red}{+} (-4-5x) \\\Leftrightarrow & 8x+12& = &-7-4-5x \\\Leftrightarrow & 8x \color{red}{+12} & = &-11 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 8x+5x& = &-11-12 \\\Leftrightarrow & 13x& = &-23 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-23}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-23}{13} & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-4x+3)& = & -3 \color{red}{+} (4+x) \\\Leftrightarrow & -12x+9& = &-3+4+x \\\Leftrightarrow & -12x \color{red}{+9} & = &1 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & -12x-x& = &1-9 \\\Leftrightarrow & -13x& = &-8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-2x+4)& = & 2 \color{red}{+} (8-3x) \\\Leftrightarrow & -10x+20& = &2+8-3x \\\Leftrightarrow & -10x \color{red}{+20} & = &10 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & -10x+3x& = &10-20 \\\Leftrightarrow & -7x& = &-10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (x+3)& = & 7 \color{red}{-} (1-5x) \\\Leftrightarrow & 3x+9& = &7-1+5x \\\Leftrightarrow & 3x \color{red}{+9} & = &6 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{+9} \color{blue}{-9} \color{blue}{-5x} & = &6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-9} \\\Leftrightarrow & 3x-5x& = &6-9 \\\Leftrightarrow & -2x& = &-3 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-3}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{3}{2} & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x-2)& = & -8 \color{red}{+} (3+x) \\\Leftrightarrow & -5x-10& = &-8+3+x \\\Leftrightarrow & -5x \color{red}{-10} & = &-5 \color{red}{+x} \\\Leftrightarrow & -5x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -5x-x& = &-5+10 \\\Leftrightarrow & -6x& = &5 \\\Leftrightarrow & \frac{-6x}{ \color{red}{-6} }& = &\frac{5}{ \color{red}{-6} } \\\Leftrightarrow & x = \frac{-5}{6} & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x-2)& = & -13 \color{red}{+} (4+3x) \\\Leftrightarrow & -8x-4& = &-13+4+3x \\\Leftrightarrow & -8x \color{red}{-4} & = &-9 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &-9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & -8x-3x& = &-9+4 \\\Leftrightarrow & -11x& = &-5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (5x+4)& = & 5 \color{red}{+} (-5+x) \\\Leftrightarrow & 30x+24& = &5-5+x \\\Leftrightarrow & 30x \color{red}{+24} & = &0 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 30x-x& = &0-24 \\\Leftrightarrow & 29x& = &-24 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-24}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-24}{29} & & \\ & V = \left\{ \frac{-24}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (5x-1)& = & -3 \color{red}{-} (-12-3x) \\\Leftrightarrow & 10x-2& = &-3+12+3x \\\Leftrightarrow & 10x \color{red}{-2} & = &9 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-2} \color{blue}{+2} \color{blue}{-3x} & = &9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+2} \\\Leftrightarrow & 10x-3x& = &9+2 \\\Leftrightarrow & 7x& = &11 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{11}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-4x+1)& = & -7 \color{red}{+} (-2+x) \\\Leftrightarrow & -20x+5& = &-7-2+x \\\Leftrightarrow & -20x \color{red}{+5} & = &-9 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & -20x-x& = &-9-5 \\\Leftrightarrow & -21x& = &-14 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-14}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x-7)& = & -4 \color{red}{-} (12+x) \\\Leftrightarrow & -30x-35& = &-4-12-x \\\Leftrightarrow & -30x \color{red}{-35} & = &-16 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & -30x+x& = &-16+35 \\\Leftrightarrow & -29x& = &19 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{19}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-19}{29} & & \\ & V = \left\{ \frac{-19}{29} \right\} & \\\end{align}\)