Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-2x+1)& = & 13 \color{red}{+} (-8+x) \\\Leftrightarrow & -12x+6& = &13-8+x \\\Leftrightarrow & -12x \color{red}{+6} & = &5 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -12x-x& = &5-6 \\\Leftrightarrow & -13x& = &-1 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-1}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-4x+6)& = & 7 \color{red}{+} (-9+x) \\\Leftrightarrow & -8x+12& = &7-9+x \\\Leftrightarrow & -8x \color{red}{+12} & = &-2 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -8x-x& = &-2-12 \\\Leftrightarrow & -9x& = &-14 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-14}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{14}{9} & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-3x-3)& = & -11 \color{red}{-} (-10+x) \\\Leftrightarrow & -12x-12& = &-11+10-x \\\Leftrightarrow & -12x \color{red}{-12} & = &-1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &-1+12 \\\Leftrightarrow & -11x& = &11 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{11}{ \color{red}{-11} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-5x-5)& = & -12 \color{red}{+} (13+x) \\\Leftrightarrow & -30x-30& = &-12+13+x \\\Leftrightarrow & -30x \color{red}{-30} & = &1 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -30x-x& = &1+30 \\\Leftrightarrow & -31x& = &31 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{31}{ \color{red}{-31} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-6x-2)& = & 14 \color{red}{+} (13+x) \\\Leftrightarrow & -24x-8& = &14+13+x \\\Leftrightarrow & -24x \color{red}{-8} & = &27 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &27 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -24x-x& = &27+8 \\\Leftrightarrow & -25x& = &35 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{35}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-7}{5} & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-2x+7)& = & 15 \color{red}{+} (4+x) \\\Leftrightarrow & -12x+42& = &15+4+x \\\Leftrightarrow & -12x \color{red}{+42} & = &19 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -12x-x& = &19-42 \\\Leftrightarrow & -13x& = &-23 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-23}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{23}{13} & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-6x+6)& = & -5 \color{red}{-} (5+x) \\\Leftrightarrow & -12x+12& = &-5-5-x \\\Leftrightarrow & -12x \color{red}{+12} & = &-10 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &-10-12 \\\Leftrightarrow & -11x& = &-22 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-22}{ \color{red}{-11} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (3x+3)& = & -13 \color{red}{+} (6+x) \\\Leftrightarrow & 6x+6& = &-13+6+x \\\Leftrightarrow & 6x \color{red}{+6} & = &-7 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 6x-x& = &-7-6 \\\Leftrightarrow & 5x& = &-13 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-13}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-13}{5} & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (2x+6)& = & -10 \color{red}{+} (-6-3x) \\\Leftrightarrow & 10x+30& = &-10-6-3x \\\Leftrightarrow & 10x \color{red}{+30} & = &-16 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+30} \color{blue}{-30} \color{blue}{+3x} & = &-16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-30} \\\Leftrightarrow & 10x+3x& = &-16-30 \\\Leftrightarrow & 13x& = &-46 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-46}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-46}{13} & & \\ & V = \left\{ \frac{-46}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-4x-2)& = & -10 \color{red}{-} (-11+x) \\\Leftrightarrow & -24x-12& = &-10+11-x \\\Leftrightarrow & -24x \color{red}{-12} & = &1 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -24x+x& = &1+12 \\\Leftrightarrow & -23x& = &13 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{13}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-13}{23} & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (5x+6)& = & -8 \color{red}{-} (-10+x) \\\Leftrightarrow & 15x+18& = &-8+10-x \\\Leftrightarrow & 15x \color{red}{+18} & = &2 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 15x+x& = &2-18 \\\Leftrightarrow & 16x& = &-16 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{-16}{ \color{red}{16} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (2x-6)& = & -10 \color{red}{+} (14+x) \\\Leftrightarrow & 8x-24& = &-10+14+x \\\Leftrightarrow & 8x \color{red}{-24} & = &4 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 8x-x& = &4+24 \\\Leftrightarrow & 7x& = &28 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{28}{ \color{red}{7} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)