Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-4x+5)& = & -2 \color{red}{+} (-5+x) \\\Leftrightarrow & -20x+25& = &-2-5+x \\\Leftrightarrow & -20x \color{red}{+25} & = &-7 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -20x-x& = &-7-25 \\\Leftrightarrow & -21x& = &-32 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-32}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{32}{21} & & \\ & V = \left\{ \frac{32}{21} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x-1)& = & -9 \color{red}{-} (10+x) \\\Leftrightarrow & 5x-5& = &-9-10-x \\\Leftrightarrow & 5x \color{red}{-5} & = &-19 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & 5x+x& = &-19+5 \\\Leftrightarrow & 6x& = &-14 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{-14}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{-7}{3} & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (6x+3)& = & 14 \color{red}{-} (-8-5x) \\\Leftrightarrow & 18x+9& = &14+8+5x \\\Leftrightarrow & 18x \color{red}{+9} & = &22 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+9} \color{blue}{-9} \color{blue}{-5x} & = &22 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-9} \\\Leftrightarrow & 18x-5x& = &22-9 \\\Leftrightarrow & 13x& = &13 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{13}{ \color{red}{13} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-2x+7)& = & 3 \color{red}{-} (11-5x) \\\Leftrightarrow & -6x+21& = &3-11+5x \\\Leftrightarrow & -6x \color{red}{+21} & = &-8 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+21} \color{blue}{-21} \color{blue}{-5x} & = &-8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-21} \\\Leftrightarrow & -6x-5x& = &-8-21 \\\Leftrightarrow & -11x& = &-29 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-29}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{29}{11} & & \\ & V = \left\{ \frac{29}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (4x-3)& = & -12 \color{red}{+} (-15+3x) \\\Leftrightarrow & 8x-6& = &-12-15+3x \\\Leftrightarrow & 8x \color{red}{-6} & = &-27 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{-6} \color{blue}{+6} \color{blue}{-3x} & = &-27 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+6} \\\Leftrightarrow & 8x-3x& = &-27+6 \\\Leftrightarrow & 5x& = &-21 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-21}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-21}{5} & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (6x-6)& = & -1 \color{red}{-} (4+x) \\\Leftrightarrow & 24x-24& = &-1-4-x \\\Leftrightarrow & 24x \color{red}{-24} & = &-5 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 24x+x& = &-5+24 \\\Leftrightarrow & 25x& = &19 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{19}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{19}{25} & & \\ & V = \left\{ \frac{19}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (3x-4)& = & -13 \color{red}{+} (11-5x) \\\Leftrightarrow & 18x-24& = &-13+11-5x \\\Leftrightarrow & 18x \color{red}{-24} & = &-2 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & 18x+5x& = &-2+24 \\\Leftrightarrow & 23x& = &22 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{22}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{22}{23} & & \\ & V = \left\{ \frac{22}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (2x-7)& = & -1 \color{red}{-} (-5+x) \\\Leftrightarrow & 6x-21& = &-1+5-x \\\Leftrightarrow & 6x \color{red}{-21} & = &4 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & 6x+x& = &4+21 \\\Leftrightarrow & 7x& = &25 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{25}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{25}{7} & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-2x+2)& = & 9 \color{red}{+} (-12+x) \\\Leftrightarrow & -4x+4& = &9-12+x \\\Leftrightarrow & -4x \color{red}{+4} & = &-3 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -4x-x& = &-3-4 \\\Leftrightarrow & -5x& = &-7 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-7}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-2x-6)& = & 9 \color{red}{-} (2+x) \\\Leftrightarrow & -12x-36& = &9-2-x \\\Leftrightarrow & -12x \color{red}{-36} & = &7 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -12x+x& = &7+36 \\\Leftrightarrow & -11x& = &43 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{43}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-43}{11} & & \\ & V = \left\{ \frac{-43}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (3x+7)& = & -7 \color{red}{-} (-9+x) \\\Leftrightarrow & 6x+14& = &-7+9-x \\\Leftrightarrow & 6x \color{red}{+14} & = &2 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & 6x+x& = &2-14 \\\Leftrightarrow & 7x& = &-12 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-12}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-12}{7} & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-3x-5)& = & 8 \color{red}{-} (-12+x) \\\Leftrightarrow & -9x-15& = &8+12-x \\\Leftrightarrow & -9x \color{red}{-15} & = &20 \color{red}{-x} \\\Leftrightarrow & -9x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -9x+x& = &20+15 \\\Leftrightarrow & -8x& = &35 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{35}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-35}{8} & & \\ & V = \left\{ \frac{-35}{8} \right\} & \\\end{align}\)