Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-5x+3)& = & 15 \color{red}{-} (7+x) \\\Leftrightarrow & -20x+12& = &15-7-x \\\Leftrightarrow & -20x \color{red}{+12} & = &8 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -20x+x& = &8-12 \\\Leftrightarrow & -19x& = &-4 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-4}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{4}{19} & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (4x-3)& = & -15 \color{red}{+} (-12-5x) \\\Leftrightarrow & 8x-6& = &-15-12-5x \\\Leftrightarrow & 8x \color{red}{-6} & = &-27 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &-27 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 8x+5x& = &-27+6 \\\Leftrightarrow & 13x& = &-21 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-21}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-21}{13} & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-4x-6)& = & 1 \color{red}{+} (7+x) \\\Leftrightarrow & -12x-18& = &1+7+x \\\Leftrightarrow & -12x \color{red}{-18} & = &8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -12x-x& = &8+18 \\\Leftrightarrow & -13x& = &26 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{26}{ \color{red}{-13} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (x-2)& = & 8 \color{red}{+} (12+x) \\\Leftrightarrow & 4x-8& = &8+12+x \\\Leftrightarrow & 4x \color{red}{-8} & = &20 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 4x-x& = &20+8 \\\Leftrightarrow & 3x& = &28 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{28}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{28}{3} & & \\ & V = \left\{ \frac{28}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (3x+1)& = & 15 \color{red}{-} (6+x) \\\Leftrightarrow & 12x+4& = &15-6-x \\\Leftrightarrow & 12x \color{red}{+4} & = &9 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 12x+x& = &9-4 \\\Leftrightarrow & 13x& = &5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (x+2)& = & -5 \color{red}{+} (-6-5x) \\\Leftrightarrow & 6x+12& = &-5-6-5x \\\Leftrightarrow & 6x \color{red}{+12} & = &-11 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 6x+5x& = &-11-12 \\\Leftrightarrow & 11x& = &-23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-23}{11} & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-4x-7)& = & 9 \color{red}{+} (-1+x) \\\Leftrightarrow & -20x-35& = &9-1+x \\\Leftrightarrow & -20x \color{red}{-35} & = &8 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & -20x-x& = &8+35 \\\Leftrightarrow & -21x& = &43 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{43}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-43}{21} & & \\ & V = \left\{ \frac{-43}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (5x-1)& = & -5 \color{red}{-} (14+x) \\\Leftrightarrow & 20x-4& = &-5-14-x \\\Leftrightarrow & 20x \color{red}{-4} & = &-19 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 20x+x& = &-19+4 \\\Leftrightarrow & 21x& = &-15 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-15}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (3x-5)& = & -11 \color{red}{+} (2+x) \\\Leftrightarrow & 12x-20& = &-11+2+x \\\Leftrightarrow & 12x \color{red}{-20} & = &-9 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 12x-x& = &-9+20 \\\Leftrightarrow & 11x& = &11 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{11}{ \color{red}{11} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (4x+1)& = & 10 \color{red}{+} (-9+3x) \\\Leftrightarrow & 20x+5& = &10-9+3x \\\Leftrightarrow & 20x \color{red}{+5} & = &1 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{+5} \color{blue}{-5} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-5} \\\Leftrightarrow & 20x-3x& = &1-5 \\\Leftrightarrow & 17x& = &-4 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-4}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-4}{17} & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (x-7)& = & 2 \color{red}{+} (-12+x) \\\Leftrightarrow & 4x-28& = &2-12+x \\\Leftrightarrow & 4x \color{red}{-28} & = &-10 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 4x-x& = &-10+28 \\\Leftrightarrow & 3x& = &18 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{18}{ \color{red}{3} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x-4)& = & 8 \color{red}{-} (-12+x) \\\Leftrightarrow & 12x-24& = &8+12-x \\\Leftrightarrow & 12x \color{red}{-24} & = &20 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 12x+x& = &20+24 \\\Leftrightarrow & 13x& = &44 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{44}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{44}{13} & & \\ & V = \left\{ \frac{44}{13} \right\} & \\\end{align}\)