Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-2x+3)& = & -14 \color{red}{+} (8+x) \\\Leftrightarrow & -6x+9& = &-14+8+x \\\Leftrightarrow & -6x \color{red}{+9} & = &-6 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & -6x-x& = &-6-9 \\\Leftrightarrow & -7x& = &-15 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-15}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{15}{7} & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-x-2)& = & 11 \color{red}{-} (6-4x) \\\Leftrightarrow & -5x-10& = &11-6+4x \\\Leftrightarrow & -5x \color{red}{-10} & = &5 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-10} \color{blue}{+10} \color{blue}{-4x} & = &5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+10} \\\Leftrightarrow & -5x-4x& = &5+10 \\\Leftrightarrow & -9x& = &15 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{15}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-5}{3} & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (3x+6)& = & -10 \color{red}{+} (5-5x) \\\Leftrightarrow & 18x+36& = &-10+5-5x \\\Leftrightarrow & 18x \color{red}{+36} & = &-5 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & 18x+5x& = &-5-36 \\\Leftrightarrow & 23x& = &-41 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-41}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-41}{23} & & \\ & V = \left\{ \frac{-41}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-3x+1)& = & -12 \color{red}{-} (6-2x) \\\Leftrightarrow & -15x+5& = &-12-6+2x \\\Leftrightarrow & -15x \color{red}{+5} & = &-18 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &-18 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & -15x-2x& = &-18-5 \\\Leftrightarrow & -17x& = &-23 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-23}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{23}{17} & & \\ & V = \left\{ \frac{23}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-2x+2)& = & 14 \color{red}{-} (-10+x) \\\Leftrightarrow & -10x+10& = &14+10-x \\\Leftrightarrow & -10x \color{red}{+10} & = &24 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &24 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -10x+x& = &24-10 \\\Leftrightarrow & -9x& = &14 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{14}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-14}{9} & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-4x-3)& = & 1 \color{red}{+} (-9+x) \\\Leftrightarrow & -8x-6& = &1-9+x \\\Leftrightarrow & -8x \color{red}{-6} & = &-8 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -8x-x& = &-8+6 \\\Leftrightarrow & -9x& = &-2 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-2}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{2}{9} & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-6x-3)& = & 1 \color{red}{-} (4+x) \\\Leftrightarrow & -24x-12& = &1-4-x \\\Leftrightarrow & -24x \color{red}{-12} & = &-3 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -24x+x& = &-3+12 \\\Leftrightarrow & -23x& = &9 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{9}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-9}{23} & & \\ & V = \left\{ \frac{-9}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-3x+5)& = & -13 \color{red}{+} (-9+x) \\\Leftrightarrow & -12x+20& = &-13-9+x \\\Leftrightarrow & -12x \color{red}{+20} & = &-22 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -12x-x& = &-22-20 \\\Leftrightarrow & -13x& = &-42 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-42}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{42}{13} & & \\ & V = \left\{ \frac{42}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (4x+1)& = & 6 \color{red}{-} (9+x) \\\Leftrightarrow & 20x+5& = &6-9-x \\\Leftrightarrow & 20x \color{red}{+5} & = &-3 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & 20x+x& = &-3-5 \\\Leftrightarrow & 21x& = &-8 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-8}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-8}{21} & & \\ & V = \left\{ \frac{-8}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-4x-3)& = & -7 \color{red}{+} (-4+x) \\\Leftrightarrow & -24x-18& = &-7-4+x \\\Leftrightarrow & -24x \color{red}{-18} & = &-11 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -24x-x& = &-11+18 \\\Leftrightarrow & -25x& = &7 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{7}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-7}{25} & & \\ & V = \left\{ \frac{-7}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x+1)& = & 13 \color{red}{+} (-11+x) \\\Leftrightarrow & -12x+6& = &13-11+x \\\Leftrightarrow & -12x \color{red}{+6} & = &2 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -12x-x& = &2-6 \\\Leftrightarrow & -13x& = &-4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x-7)& = & 3 \color{red}{-} (6+x) \\\Leftrightarrow & -30x-35& = &3-6-x \\\Leftrightarrow & -30x \color{red}{-35} & = &-3 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & -30x+x& = &-3+35 \\\Leftrightarrow & -29x& = &32 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{32}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-32}{29} & & \\ & V = \left\{ \frac{-32}{29} \right\} & \\\end{align}\)