Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+15}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-x } & = & -6 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -6 \color{blue}{-15} \\\Leftrightarrow &x & = &-21\\\Leftrightarrow & \color{red}{}x & = &-21\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -21 \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-6}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x } & = & -12 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -12 \color{blue}{+6} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-12}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-12}\color{blue}{+12-x } & = & 4 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 4 \color{blue}{+12} \\\Leftrightarrow &-5x & = &16\\\Leftrightarrow & \color{red}{-5}x & = &16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-15}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-x } & = & -13 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -13 \color{blue}{+15} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-8}& = & -15 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8-12x } & = & -15 \color{red}{ +12x }\color{blue}{+8-12x } \\\Leftrightarrow & 5x \color{blue}{-12x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &-7x & = &-7\\\Leftrightarrow & \color{red}{-7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+10}& = & -14 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10+10x } & = & -14 \color{red}{ -10x }\color{blue}{-10+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & -14 \color{blue}{-10} \\\Leftrightarrow &9x & = &-24\\\Leftrightarrow & \color{red}{9}x & = &-24\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-24}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-6}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6-11x } & = & -5 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & x \color{blue}{-11x } & = & -5 \color{blue}{+6} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+4}& = & 9 \color{red}{ +8x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4-8x } & = & 9 \color{red}{ +8x }\color{blue}{-4-8x } \\\Leftrightarrow & 13x \color{blue}{-8x } & = & 9 \color{blue}{-4} \\\Leftrightarrow &5x & = &5\\\Leftrightarrow & \color{red}{5}x & = &5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{5}{5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-8}& = & -12 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8-10x } & = & -12 \color{red}{ +10x }\color{blue}{+8-10x } \\\Leftrightarrow & 11x \color{blue}{-10x } & = & -12 \color{blue}{+8} \\\Leftrightarrow &x & = &-4\\\Leftrightarrow & \color{red}{}x & = &-4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -4 \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+6}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6-11x } & = & 11 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & 13x \color{blue}{-11x } & = & 11 \color{blue}{-6} \\\Leftrightarrow &2x & = &5\\\Leftrightarrow & \color{red}{2}x & = &5\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{5}{2} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+3}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-x } & = & 1 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 1 \color{blue}{-3} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-4}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4-5x } & = & -15 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & -7x \color{blue}{-5x } & = & -15 \color{blue}{+4} \\\Leftrightarrow &-12x & = &-11\\\Leftrightarrow & \color{red}{-12}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-11}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{12} } & & \\ & V = \left\{ \frac{11}{12} \right\} & \\\end{align}\)