Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x-4)& = & 11 \color{red}{-} (-9+x) \\\Leftrightarrow & -30x-24& = &11+9-x \\\Leftrightarrow & -30x \color{red}{-24} & = &20 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -30x+x& = &20+24 \\\Leftrightarrow & -29x& = &44 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{44}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-44}{29} & & \\ & V = \left\{ \frac{-44}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (2x-1)& = & 1 \color{red}{+} (-4+5x) \\\Leftrightarrow & 6x-3& = &1-4+5x \\\Leftrightarrow & 6x \color{red}{-3} & = &-3 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &-3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & 6x-5x& = &-3+3 \\\Leftrightarrow & x& = &0 \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-3x+3)& = & -3 \color{red}{+} (-12-2x) \\\Leftrightarrow & -15x+15& = &-3-12-2x \\\Leftrightarrow & -15x \color{red}{+15} & = &-15 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{+2x} & = &-15 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-15} \\\Leftrightarrow & -15x+2x& = &-15-15 \\\Leftrightarrow & -13x& = &-30 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-30}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{30}{13} & & \\ & V = \left\{ \frac{30}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (6x+6)& = & 9 \color{red}{+} (-1-5x) \\\Leftrightarrow & 18x+18& = &9-1-5x \\\Leftrightarrow & 18x \color{red}{+18} & = &8 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & 18x+5x& = &8-18 \\\Leftrightarrow & 23x& = &-10 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-10}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-10}{23} & & \\ & V = \left\{ \frac{-10}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x-3)& = & 9 \color{red}{-} (-9-5x) \\\Leftrightarrow & -18x-9& = &9+9+5x \\\Leftrightarrow & -18x \color{red}{-9} & = &18 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-9} \color{blue}{+9} \color{blue}{-5x} & = &18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+9} \\\Leftrightarrow & -18x-5x& = &18+9 \\\Leftrightarrow & -23x& = &27 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{27}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-27}{23} & & \\ & V = \left\{ \frac{-27}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-2x+4)& = & -7 \color{red}{-} (-4-3x) \\\Leftrightarrow & -4x+8& = &-7+4+3x \\\Leftrightarrow & -4x \color{red}{+8} & = &-3 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -4x-3x& = &-3-8 \\\Leftrightarrow & -7x& = &-11 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-11}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (6x-5)& = & 9 \color{red}{+} (3+x) \\\Leftrightarrow & 24x-20& = &9+3+x \\\Leftrightarrow & 24x \color{red}{-20} & = &12 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 24x-x& = &12+20 \\\Leftrightarrow & 23x& = &32 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{32}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{32}{23} & & \\ & V = \left\{ \frac{32}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (2x+2)& = & 1 \color{red}{+} (1+x) \\\Leftrightarrow & 12x+12& = &1+1+x \\\Leftrightarrow & 12x \color{red}{+12} & = &2 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &2-12 \\\Leftrightarrow & 11x& = &-10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (2x+7)& = & -5 \color{red}{-} (-9+3x) \\\Leftrightarrow & 4x+14& = &-5+9-3x \\\Leftrightarrow & 4x \color{red}{+14} & = &4 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & 4x+3x& = &4-14 \\\Leftrightarrow & 7x& = &-10 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-10}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-6x+6)& = & -6 \color{red}{+} (-5+x) \\\Leftrightarrow & -36x+36& = &-6-5+x \\\Leftrightarrow & -36x \color{red}{+36} & = &-11 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -36x-x& = &-11-36 \\\Leftrightarrow & -37x& = &-47 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-47}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{47}{37} & & \\ & V = \left\{ \frac{47}{37} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-3x+1)& = & 5 \color{red}{-} (7+4x) \\\Leftrightarrow & -15x+5& = &5-7-4x \\\Leftrightarrow & -15x \color{red}{+5} & = &-2 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{+5} \color{blue}{-5} \color{blue}{+4x} & = &-2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-5} \\\Leftrightarrow & -15x+4x& = &-2-5 \\\Leftrightarrow & -11x& = &-7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-3x-3)& = & 6 \color{red}{+} (2-5x) \\\Leftrightarrow & -18x-18& = &6+2-5x \\\Leftrightarrow & -18x \color{red}{-18} & = &8 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & -18x+5x& = &8+18 \\\Leftrightarrow & -13x& = &26 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{26}{ \color{red}{-13} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)