Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-x-2)& = & 4 \color{red}{+} (15-5x) \\\Leftrightarrow & -6x-12& = &4+15-5x \\\Leftrightarrow & -6x \color{red}{-12} & = &19 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &19 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -6x+5x& = &19+12 \\\Leftrightarrow & -x& = &31 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{31}{ \color{red}{-1} } \\\Leftrightarrow & x = -31 & & \\ & V = \left\{ -31 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (x+6)& = & -15 \color{red}{+} (-1-3x) \\\Leftrightarrow & 4x+24& = &-15-1-3x \\\Leftrightarrow & 4x \color{red}{+24} & = &-16 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+24} \color{blue}{-24} \color{blue}{+3x} & = &-16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-24} \\\Leftrightarrow & 4x+3x& = &-16-24 \\\Leftrightarrow & 7x& = &-40 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-40}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-40}{7} & & \\ & V = \left\{ \frac{-40}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-x+6)& = & -4 \color{red}{-} (-7-5x) \\\Leftrightarrow & -3x+18& = &-4+7+5x \\\Leftrightarrow & -3x \color{red}{+18} & = &3 \color{red}{+5x} \\\Leftrightarrow & -3x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & -3x-5x& = &3-18 \\\Leftrightarrow & -8x& = &-15 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{-15}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{15}{8} & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (3x-5)& = & -7 \color{red}{-} (-9+4x) \\\Leftrightarrow & 15x-25& = &-7+9-4x \\\Leftrightarrow & 15x \color{red}{-25} & = &2 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{-25} \color{blue}{+25} \color{blue}{+4x} & = &2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+25} \\\Leftrightarrow & 15x+4x& = &2+25 \\\Leftrightarrow & 19x& = &27 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{27}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{27}{19} & & \\ & V = \left\{ \frac{27}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (6x+6)& = & -15 \color{red}{+} (-15+x) \\\Leftrightarrow & 18x+18& = &-15-15+x \\\Leftrightarrow & 18x \color{red}{+18} & = &-30 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-30 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 18x-x& = &-30-18 \\\Leftrightarrow & 17x& = &-48 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-48}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-48}{17} & & \\ & V = \left\{ \frac{-48}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-3x-1)& = & -7 \color{red}{-} (1+x) \\\Leftrightarrow & -12x-4& = &-7-1-x \\\Leftrightarrow & -12x \color{red}{-4} & = &-8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -12x+x& = &-8+4 \\\Leftrightarrow & -11x& = &-4 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-4}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (x-2)& = & -1 \color{red}{+} (10-3x) \\\Leftrightarrow & 4x-8& = &-1+10-3x \\\Leftrightarrow & 4x \color{red}{-8} & = &9 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & 4x+3x& = &9+8 \\\Leftrightarrow & 7x& = &17 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{17}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (5x-2)& = & 5 \color{red}{+} (-7+x) \\\Leftrightarrow & 15x-6& = &5-7+x \\\Leftrightarrow & 15x \color{red}{-6} & = &-2 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 15x-x& = &-2+6 \\\Leftrightarrow & 14x& = &4 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{4}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-3x+4)& = & -3 \color{red}{+} (-2+x) \\\Leftrightarrow & -6x+8& = &-3-2+x \\\Leftrightarrow & -6x \color{red}{+8} & = &-5 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -6x-x& = &-5-8 \\\Leftrightarrow & -7x& = &-13 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-13}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-x-6)& = & -14 \color{red}{-} (-15-4x) \\\Leftrightarrow & -5x-30& = &-14+15+4x \\\Leftrightarrow & -5x \color{red}{-30} & = &1 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-30} \color{blue}{+30} \color{blue}{-4x} & = &1 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+30} \\\Leftrightarrow & -5x-4x& = &1+30 \\\Leftrightarrow & -9x& = &31 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{31}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-31}{9} & & \\ & V = \left\{ \frac{-31}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (5x+7)& = & 13 \color{red}{-} (13+4x) \\\Leftrightarrow & 25x+35& = &13-13-4x \\\Leftrightarrow & 25x \color{red}{+35} & = &0 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{+35} \color{blue}{-35} \color{blue}{+4x} & = &0 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-35} \\\Leftrightarrow & 25x+4x& = &0-35 \\\Leftrightarrow & 29x& = &-35 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-35}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-35}{29} & & \\ & V = \left\{ \frac{-35}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-4x-5)& = & -2 \color{red}{-} (2+x) \\\Leftrightarrow & -20x-25& = &-2-2-x \\\Leftrightarrow & -20x \color{red}{-25} & = &-4 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & -20x+x& = &-4+25 \\\Leftrightarrow & -19x& = &21 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{21}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-21}{19} & & \\ & V = \left\{ \frac{-21}{19} \right\} & \\\end{align}\)