Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-4x+4)& = & 7 \color{red}{+} (3-5x) \\\Leftrightarrow & -8x+8& = &7+3-5x \\\Leftrightarrow & -8x \color{red}{+8} & = &10 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{+5x} & = &10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-8} \\\Leftrightarrow & -8x+5x& = &10-8 \\\Leftrightarrow & -3x& = &2 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{2}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x+1)& = & 14 \color{red}{-} (10+3x) \\\Leftrightarrow & -4x+4& = &14-10-3x \\\Leftrightarrow & -4x \color{red}{+4} & = &4 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & -4x+3x& = &4-4 \\\Leftrightarrow & -x& = &0 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{0}{ \color{red}{-1} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x+2)& = & 9 \color{red}{-} (11-2x) \\\Leftrightarrow & 15x+10& = &9-11+2x \\\Leftrightarrow & 15x \color{red}{+10} & = &-2 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+10} \color{blue}{-10} \color{blue}{-2x} & = &-2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-10} \\\Leftrightarrow & 15x-2x& = &-2-10 \\\Leftrightarrow & 13x& = &-12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (6x+7)& = & -8 \color{red}{-} (-14+x) \\\Leftrightarrow & 12x+14& = &-8+14-x \\\Leftrightarrow & 12x \color{red}{+14} & = &6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & 12x+x& = &6-14 \\\Leftrightarrow & 13x& = &-8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (3x+1)& = & -4 \color{red}{+} (-2-5x) \\\Leftrightarrow & 6x+2& = &-4-2-5x \\\Leftrightarrow & 6x \color{red}{+2} & = &-6 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+2} \color{blue}{-2} \color{blue}{+5x} & = &-6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-2} \\\Leftrightarrow & 6x+5x& = &-6-2 \\\Leftrightarrow & 11x& = &-8 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-8}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-8}{11} & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-x-4)& = & -13 \color{red}{-} (-3-3x) \\\Leftrightarrow & -4x-16& = &-13+3+3x \\\Leftrightarrow & -4x \color{red}{-16} & = &-10 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-16} \color{blue}{+16} \color{blue}{-3x} & = &-10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+16} \\\Leftrightarrow & -4x-3x& = &-10+16 \\\Leftrightarrow & -7x& = &6 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{6}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x-6)& = & 13 \color{red}{-} (15+x) \\\Leftrightarrow & 8x-24& = &13-15-x \\\Leftrightarrow & 8x \color{red}{-24} & = &-2 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 8x+x& = &-2+24 \\\Leftrightarrow & 9x& = &22 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{22}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{22}{9} & & \\ & V = \left\{ \frac{22}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-6x-1)& = & 3 \color{red}{+} (10+x) \\\Leftrightarrow & -24x-4& = &3+10+x \\\Leftrightarrow & -24x \color{red}{-4} & = &13 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -24x-x& = &13+4 \\\Leftrightarrow & -25x& = &17 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{17}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-17}{25} & & \\ & V = \left\{ \frac{-17}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x-3)& = & 2 \color{red}{+} (13-5x) \\\Leftrightarrow & 18x-18& = &2+13-5x \\\Leftrightarrow & 18x \color{red}{-18} & = &15 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & 18x+5x& = &15+18 \\\Leftrightarrow & 23x& = &33 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{33}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{33}{23} & & \\ & V = \left\{ \frac{33}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (6x-2)& = & -1 \color{red}{-} (8+x) \\\Leftrightarrow & 12x-4& = &-1-8-x \\\Leftrightarrow & 12x \color{red}{-4} & = &-9 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 12x+x& = &-9+4 \\\Leftrightarrow & 13x& = &-5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-5x+6)& = & -7 \color{red}{+} (5+4x) \\\Leftrightarrow & -25x+30& = &-7+5+4x \\\Leftrightarrow & -25x \color{red}{+30} & = &-2 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{+30} \color{blue}{-30} \color{blue}{-4x} & = &-2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-30} \\\Leftrightarrow & -25x-4x& = &-2-30 \\\Leftrightarrow & -29x& = &-32 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-32}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{32}{29} & & \\ & V = \left\{ \frac{32}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-3x+2)& = & -13 \color{red}{+} (9+x) \\\Leftrightarrow & -12x+8& = &-13+9+x \\\Leftrightarrow & -12x \color{red}{+8} & = &-4 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -12x-x& = &-4-8 \\\Leftrightarrow & -13x& = &-12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)