Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-3}& = & -8 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-3}\color{blue}{+3+7x } & = & -8 \color{red}{ -7x }\color{blue}{+3+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -8 \color{blue}{+3} \\\Leftrightarrow &15x & = &-5\\\Leftrightarrow & \color{red}{15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-12}\color{blue}{+12-x } & = & -8 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+5}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5-7x } & = & 7 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 7 \color{blue}{-5} \\\Leftrightarrow &-20x & = &2\\\Leftrightarrow & \color{red}{-20}x & = &2\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{2}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+2}& = & 6 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2-3x } & = & 6 \color{red}{ +3x }\color{blue}{-2-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+15}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15-x } & = & -1 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &-15x & = &-16\\\Leftrightarrow & \color{red}{-15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{16}{15} } & & \\ & V = \left\{ \frac{16}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6-x } & = & 13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &-14x & = &19\\\Leftrightarrow & \color{red}{-14}x & = &19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{14} } & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-x } & = & 10 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &-9x & = &23\\\Leftrightarrow & \color{red}{-9}x & = &23\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{23}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{9} } & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+4}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-x } & = & -1 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -1 \color{blue}{-4} \\\Leftrightarrow &-8x & = &-5\\\Leftrightarrow & \color{red}{-8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-15}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15-x } & = & -7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &3x & = &8\\\Leftrightarrow & \color{red}{3}x & = &8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+5}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5-x } & = & 4 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &-14x & = &-1\\\Leftrightarrow & \color{red}{-14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-7}& = & 2 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7+13x } & = & 2 \color{red}{ -13x }\color{blue}{+7+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 2 \color{blue}{+7} \\\Leftrightarrow &20x & = &9\\\Leftrightarrow & \color{red}{20}x & = &9\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{9}{20} \\\Leftrightarrow & \color{green}{ x = \frac{9}{20} } & & \\ & V = \left\{ \frac{9}{20} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+11}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-x } & = & -3 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -3 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-14\\\Leftrightarrow & \color{red}{-3}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)