Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+8}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+8}\color{blue}{-8-11x } & = & -3 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &4x & = &-11\\\Leftrightarrow & \color{red}{4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-11}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+8}& = & 15 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+8}\color{blue}{-8-10x } & = & 15 \color{red}{ +10x }\color{blue}{-8-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 15 \color{blue}{-8} \\\Leftrightarrow &-19x & = &7\\\Leftrightarrow & \color{red}{-19}x & = &7\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{7}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{19} } & & \\ & V = \left\{ \frac{-7}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+8}& = & -13 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8+15x } & = & -13 \color{red}{ -15x }\color{blue}{-8+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &19x & = &-21\\\Leftrightarrow & \color{red}{19}x & = &-21\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-21}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{19} } & & \\ & V = \left\{ \frac{-21}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+12}& = & -6 \color{red}{ +3x } \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12-3x } & = & -6 \color{red}{ +3x }\color{blue}{-12-3x } \\\Leftrightarrow & 11x \color{blue}{-3x } & = & -6 \color{blue}{-12} \\\Leftrightarrow &8x & = &-18\\\Leftrightarrow & \color{red}{8}x & = &-18\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-18}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-15}& = & -7 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15+6x } & = & -7 \color{red}{ -6x }\color{blue}{+15+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &19x & = &8\\\Leftrightarrow & \color{red}{19}x & = &8\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{8}{19} \\\Leftrightarrow & \color{green}{ x = \frac{8}{19} } & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-13}& = & 6 \color{red}{ -8x } \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13+8x } & = & 6 \color{red}{ -8x }\color{blue}{+13+8x } \\\Leftrightarrow & -x \color{blue}{+8x } & = & 6 \color{blue}{+13} \\\Leftrightarrow &7x & = &19\\\Leftrightarrow & \color{red}{7}x & = &19\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{19}{7} \\\Leftrightarrow & \color{green}{ x = \frac{19}{7} } & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+3}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-x } & = & 6 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 6 \color{blue}{-3} \\\Leftrightarrow &-4x & = &3\\\Leftrightarrow & \color{red}{-4}x & = &3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+10}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10-x } & = & 5 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 5 \color{blue}{-10} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{-5}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-x } & = & 14 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &-10x & = &19\\\Leftrightarrow & \color{red}{-10}x & = &19\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{19}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{10} } & & \\ & V = \left\{ \frac{-19}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-7}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-7}\color{blue}{+7-x } & = & -13 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -13 \color{blue}{+7} \\\Leftrightarrow &-9x & = &-6\\\Leftrightarrow & \color{red}{-9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-10}& = & 7 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-8x } & = & 7 \color{red}{ +8x }\color{blue}{+10-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 7 \color{blue}{+10} \\\Leftrightarrow &-15x & = &17\\\Leftrightarrow & \color{red}{-15}x & = &17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{15} } & & \\ & V = \left\{ \frac{-17}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+7}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7-x } & = & 13 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & 13 \color{blue}{-7} \\\Leftrightarrow &14x & = &6\\\Leftrightarrow & \color{red}{14}x & = &6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)