Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-3x-5)& = & -1 \color{red}{+} (9-5x) \\\Leftrightarrow & -18x-30& = &-1+9-5x \\\Leftrightarrow & -18x \color{red}{-30} & = &8 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-30} \color{blue}{+30} \color{blue}{+5x} & = &8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+30} \\\Leftrightarrow & -18x+5x& = &8+30 \\\Leftrightarrow & -13x& = &38 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{38}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-38}{13} & & \\ & V = \left\{ \frac{-38}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-4x+1)& = & 8 \color{red}{-} (10+x) \\\Leftrightarrow & -16x+4& = &8-10-x \\\Leftrightarrow & -16x \color{red}{+4} & = &-2 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -16x+x& = &-2-4 \\\Leftrightarrow & -15x& = &-6 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{-6}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (3x-5)& = & 8 \color{red}{-} (11+x) \\\Leftrightarrow & 18x-30& = &8-11-x \\\Leftrightarrow & 18x \color{red}{-30} & = &-3 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 18x+x& = &-3+30 \\\Leftrightarrow & 19x& = &27 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{27}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{27}{19} & & \\ & V = \left\{ \frac{27}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (4x+1)& = & 1 \color{red}{+} (-14-3x) \\\Leftrightarrow & 16x+4& = &1-14-3x \\\Leftrightarrow & 16x \color{red}{+4} & = &-13 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-13 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 16x+3x& = &-13-4 \\\Leftrightarrow & 19x& = &-17 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-17}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-17}{19} & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x-2)& = & 8 \color{red}{-} (2-5x) \\\Leftrightarrow & 36x-12& = &8-2+5x \\\Leftrightarrow & 36x \color{red}{-12} & = &6 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 36x-5x& = &6+12 \\\Leftrightarrow & 31x& = &18 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{18}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{18}{31} & & \\ & V = \left\{ \frac{18}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-4x+5)& = & 12 \color{red}{-} (6+x) \\\Leftrightarrow & -24x+30& = &12-6-x \\\Leftrightarrow & -24x \color{red}{+30} & = &6 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -24x+x& = &6-30 \\\Leftrightarrow & -23x& = &-24 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-24}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{24}{23} & & \\ & V = \left\{ \frac{24}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-5x-7)& = & -9 \color{red}{+} (10+4x) \\\Leftrightarrow & -15x-21& = &-9+10+4x \\\Leftrightarrow & -15x \color{red}{-21} & = &1 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{-21} \color{blue}{+21} \color{blue}{-4x} & = &1 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+21} \\\Leftrightarrow & -15x-4x& = &1+21 \\\Leftrightarrow & -19x& = &22 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{22}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-22}{19} & & \\ & V = \left\{ \frac{-22}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (x+3)& = & -5 \color{red}{+} (-5+3x) \\\Leftrightarrow & 2x+6& = &-5-5+3x \\\Leftrightarrow & 2x \color{red}{+6} & = &-10 \color{red}{+3x} \\\Leftrightarrow & 2x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &-10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & 2x-3x& = &-10-6 \\\Leftrightarrow & -x& = &-16 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-16}{ \color{red}{-1} } \\\Leftrightarrow & x = 16 & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x-7)& = & -11 \color{red}{-} (-9+x) \\\Leftrightarrow & 9x-21& = &-11+9-x \\\Leftrightarrow & 9x \color{red}{-21} & = &-2 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & 9x+x& = &-2+21 \\\Leftrightarrow & 10x& = &19 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{19}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{19}{10} & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (6x-7)& = & -3 \color{red}{+} (-5+x) \\\Leftrightarrow & 18x-21& = &-3-5+x \\\Leftrightarrow & 18x \color{red}{-21} & = &-8 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 18x-x& = &-8+21 \\\Leftrightarrow & 17x& = &13 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{13}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{13}{17} & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (x+2)& = & 1 \color{red}{-} (7+3x) \\\Leftrightarrow & 4x+8& = &1-7-3x \\\Leftrightarrow & 4x \color{red}{+8} & = &-6 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &-6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & 4x+3x& = &-6-8 \\\Leftrightarrow & 7x& = &-14 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-14}{ \color{red}{7} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x+5)& = & 10 \color{red}{+} (2+x) \\\Leftrightarrow & -10x+25& = &10+2+x \\\Leftrightarrow & -10x \color{red}{+25} & = &12 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -10x-x& = &12-25 \\\Leftrightarrow & -11x& = &-13 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-13}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{13}{11} & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)