Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-15}& = & -8 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15+13x } & = & -8 \color{red}{ -13x }\color{blue}{+15+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -8 \color{blue}{+15} \\\Leftrightarrow &27x & = &7\\\Leftrightarrow & \color{red}{27}x & = &7\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{7}{27} \\\Leftrightarrow & \color{green}{ x = \frac{7}{27} } & & \\ & V = \left\{ \frac{7}{27} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+1}& = & 3 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1+7x } & = & 3 \color{red}{ -7x }\color{blue}{-1+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 3 \color{blue}{-1} \\\Leftrightarrow &22x & = &2\\\Leftrightarrow & \color{red}{22}x & = &2\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{2}{22} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-7}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-7}\color{blue}{+7-x } & = & -4 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -4 \color{blue}{+7} \\\Leftrightarrow &-10x & = &3\\\Leftrightarrow & \color{red}{-10}x & = &3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+13}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13-11x } & = & 10 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 10 \color{blue}{-13} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-7}& = & 14 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7+8x } & = & 14 \color{red}{ -8x }\color{blue}{+7+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &11x & = &21\\\Leftrightarrow & \color{red}{11}x & = &21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11-x } & = & 3 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 3 \color{blue}{-11} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+5}& = & 3 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5+7x } & = & 3 \color{red}{ -7x }\color{blue}{-5+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 3 \color{blue}{-5} \\\Leftrightarrow &15x & = &-2\\\Leftrightarrow & \color{red}{15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-5}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5-x } & = & -8 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -8 \color{blue}{+5} \\\Leftrightarrow &8x & = &-3\\\Leftrightarrow & \color{red}{8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+11}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11-x } & = & 11 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 11 \color{blue}{-11} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{-3}& = & -3 \color{red}{ +15x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3-15x } & = & -3 \color{red}{ +15x }\color{blue}{+3-15x } \\\Leftrightarrow & x \color{blue}{-15x } & = & -3 \color{blue}{+3} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+6}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6-7x } & = & 12 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 12 \color{blue}{-6} \\\Leftrightarrow &8x & = &6\\\Leftrightarrow & \color{red}{8}x & = &6\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{6}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-4}& = & -15 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4-12x } & = & -15 \color{red}{ +12x }\color{blue}{+4-12x } \\\Leftrightarrow & 5x \color{blue}{-12x } & = & -15 \color{blue}{+4} \\\Leftrightarrow &-7x & = &-11\\\Leftrightarrow & \color{red}{-7}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)