Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (4x-6)& = & -1 \color{red}{-} (-12+x) \\\Leftrightarrow & 20x-30& = &-1+12-x \\\Leftrightarrow & 20x \color{red}{-30} & = &11 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 20x+x& = &11+30 \\\Leftrightarrow & 21x& = &41 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{41}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{41}{21} & & \\ & V = \left\{ \frac{41}{21} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-4x+6)& = & 9 \color{red}{+} (-1+3x) \\\Leftrightarrow & -16x+24& = &9-1+3x \\\Leftrightarrow & -16x \color{red}{+24} & = &8 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{+24} \color{blue}{-24} \color{blue}{-3x} & = &8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-24} \\\Leftrightarrow & -16x-3x& = &8-24 \\\Leftrightarrow & -19x& = &-16 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-16}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{16}{19} & & \\ & V = \left\{ \frac{16}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (2x-4)& = & -10 \color{red}{+} (5+x) \\\Leftrightarrow & 12x-24& = &-10+5+x \\\Leftrightarrow & 12x \color{red}{-24} & = &-5 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 12x-x& = &-5+24 \\\Leftrightarrow & 11x& = &19 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{19}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{19}{11} & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-4x+6)& = & -12 \color{red}{-} (8-5x) \\\Leftrightarrow & -8x+12& = &-12-8+5x \\\Leftrightarrow & -8x \color{red}{+12} & = &-20 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &-20 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -8x-5x& = &-20-12 \\\Leftrightarrow & -13x& = &-32 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-32}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{32}{13} & & \\ & V = \left\{ \frac{32}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (5x+1)& = & -7 \color{red}{+} (8+2x) \\\Leftrightarrow & 25x+5& = &-7+8+2x \\\Leftrightarrow & 25x \color{red}{+5} & = &1 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & 25x-2x& = &1-5 \\\Leftrightarrow & 23x& = &-4 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-4}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-4}{23} & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (5x-2)& = & -3 \color{red}{-} (12+x) \\\Leftrightarrow & 10x-4& = &-3-12-x \\\Leftrightarrow & 10x \color{red}{-4} & = &-15 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 10x+x& = &-15+4 \\\Leftrightarrow & 11x& = &-11 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-11}{ \color{red}{11} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-3x+4)& = & 7 \color{red}{-} (-11-5x) \\\Leftrightarrow & -18x+24& = &7+11+5x \\\Leftrightarrow & -18x \color{red}{+24} & = &18 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & -18x-5x& = &18-24 \\\Leftrightarrow & -23x& = &-6 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-6}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{6}{23} & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x-7)& = & 9 \color{red}{-} (-6+x) \\\Leftrightarrow & -8x-14& = &9+6-x \\\Leftrightarrow & -8x \color{red}{-14} & = &15 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & -8x+x& = &15+14 \\\Leftrightarrow & -7x& = &29 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{29}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-29}{7} & & \\ & V = \left\{ \frac{-29}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x-2)& = & -6 \color{red}{-} (-11-5x) \\\Leftrightarrow & 18x-12& = &-6+11+5x \\\Leftrightarrow & 18x \color{red}{-12} & = &5 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 18x-5x& = &5+12 \\\Leftrightarrow & 13x& = &17 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{17}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x-6)& = & 14 \color{red}{+} (6+2x) \\\Leftrightarrow & -15x-18& = &14+6+2x \\\Leftrightarrow & -15x \color{red}{-18} & = &20 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-18} \color{blue}{+18} \color{blue}{-2x} & = &20 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+18} \\\Leftrightarrow & -15x-2x& = &20+18 \\\Leftrightarrow & -17x& = &38 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{38}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-38}{17} & & \\ & V = \left\{ \frac{-38}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (2x+4)& = & -11 \color{red}{+} (-15+x) \\\Leftrightarrow & 4x+8& = &-11-15+x \\\Leftrightarrow & 4x \color{red}{+8} & = &-26 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-26 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 4x-x& = &-26-8 \\\Leftrightarrow & 3x& = &-34 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-34}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-34}{3} & & \\ & V = \left\{ \frac{-34}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (6x-7)& = & 10 \color{red}{-} (6+x) \\\Leftrightarrow & 12x-14& = &10-6-x \\\Leftrightarrow & 12x \color{red}{-14} & = &4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 12x+x& = &4+14 \\\Leftrightarrow & 13x& = &18 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{18}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)