Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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