Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (2x+2)& = & -10 \color{red}{+} (3-5x) \\\Leftrightarrow & 8x+8& = &-10+3-5x \\\Leftrightarrow & 8x \color{red}{+8} & = &-7 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+8} \color{blue}{-8} \color{blue}{+5x} & = &-7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-8} \\\Leftrightarrow & 8x+5x& = &-7-8 \\\Leftrightarrow & 13x& = &-15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-6x+3)& = & 1 \color{red}{+} (14+x) \\\Leftrightarrow & -24x+12& = &1+14+x \\\Leftrightarrow & -24x \color{red}{+12} & = &15 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -24x-x& = &15-12 \\\Leftrightarrow & -25x& = &3 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{3}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-3}{25} & & \\ & V = \left\{ \frac{-3}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-x+6)& = & 7 \color{red}{+} (2+x) \\\Leftrightarrow & -6x+36& = &7+2+x \\\Leftrightarrow & -6x \color{red}{+36} & = &9 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -6x-x& = &9-36 \\\Leftrightarrow & -7x& = &-27 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-27}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{27}{7} & & \\ & V = \left\{ \frac{27}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (4x-6)& = & 3 \color{red}{+} (-2+x) \\\Leftrightarrow & 24x-36& = &3-2+x \\\Leftrightarrow & 24x \color{red}{-36} & = &1 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 24x-x& = &1+36 \\\Leftrightarrow & 23x& = &37 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{37}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{37}{23} & & \\ & V = \left\{ \frac{37}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-5x-6)& = & 12 \color{red}{+} (-8-2x) \\\Leftrightarrow & -15x-18& = &12-8-2x \\\Leftrightarrow & -15x \color{red}{-18} & = &4 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-18} \color{blue}{+18} \color{blue}{+2x} & = &4 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+18} \\\Leftrightarrow & -15x+2x& = &4+18 \\\Leftrightarrow & -13x& = &22 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{22}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-22}{13} & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-6x-5)& = & -7 \color{red}{-} (-12+x) \\\Leftrightarrow & -18x-15& = &-7+12-x \\\Leftrightarrow & -18x \color{red}{-15} & = &5 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -18x+x& = &5+15 \\\Leftrightarrow & -17x& = &20 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{20}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-20}{17} & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (3x+5)& = & -12 \color{red}{-} (-5-5x) \\\Leftrightarrow & 6x+10& = &-12+5+5x \\\Leftrightarrow & 6x \color{red}{+10} & = &-7 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+10} \color{blue}{-10} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-10} \\\Leftrightarrow & 6x-5x& = &-7-10 \\\Leftrightarrow & x& = &-17 \\ & V = \left\{ -17 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-6x+3)& = & -11 \color{red}{-} (-5+x) \\\Leftrightarrow & -36x+18& = &-11+5-x \\\Leftrightarrow & -36x \color{red}{+18} & = &-6 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -36x+x& = &-6-18 \\\Leftrightarrow & -35x& = &-24 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-24}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{24}{35} & & \\ & V = \left\{ \frac{24}{35} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-5x+6)& = & 11 \color{red}{-} (15+x) \\\Leftrightarrow & -10x+12& = &11-15-x \\\Leftrightarrow & -10x \color{red}{+12} & = &-4 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -10x+x& = &-4-12 \\\Leftrightarrow & -9x& = &-16 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-16}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{16}{9} & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-3x-4)& = & -13 \color{red}{-} (7+x) \\\Leftrightarrow & -12x-16& = &-13-7-x \\\Leftrightarrow & -12x \color{red}{-16} & = &-20 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -12x+x& = &-20+16 \\\Leftrightarrow & -11x& = &-4 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-4}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (2x+2)& = & 2 \color{red}{+} (-9+x) \\\Leftrightarrow & 12x+12& = &2-9+x \\\Leftrightarrow & 12x \color{red}{+12} & = &-7 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &-7-12 \\\Leftrightarrow & 11x& = &-19 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-19}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-19}{11} & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-6x-4)& = & 9 \color{red}{-} (12+x) \\\Leftrightarrow & -12x-8& = &9-12-x \\\Leftrightarrow & -12x \color{red}{-8} & = &-3 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -12x+x& = &-3+8 \\\Leftrightarrow & -11x& = &5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)