Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+2}& = & 15 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2+13x } & = & 15 \color{red}{ -13x }\color{blue}{-2+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &23x & = &13\\\Leftrightarrow & \color{red}{23}x & = &13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{13}{23} } & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+13}\color{blue}{-13-x } & = & 10 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 10 \color{blue}{-13} \\\Leftrightarrow &-14x & = &-3\\\Leftrightarrow & \color{red}{-14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-7}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-7}\color{blue}{+7-x } & = & -11 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -11 \color{blue}{+7} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{+1}& = & 8 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1+8x } & = & 8 \color{red}{ -8x }\color{blue}{-1+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 8 \color{blue}{-1} \\\Leftrightarrow &17x & = &7\\\Leftrightarrow & \color{red}{17}x & = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+4}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4-x } & = & 7 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 7 \color{blue}{-4} \\\Leftrightarrow &-9x & = &3\\\Leftrightarrow & \color{red}{-9}x & = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-13}& = & 1 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13+14x } & = & 1 \color{red}{ -14x }\color{blue}{+13+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & 1 \color{blue}{+13} \\\Leftrightarrow &19x & = &14\\\Leftrightarrow & \color{red}{19}x & = &14\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{14}{19} \\\Leftrightarrow & \color{green}{ x = \frac{14}{19} } & & \\ & V = \left\{ \frac{14}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11-x } & = & -14 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &x & = &-25\\\Leftrightarrow & \color{red}{}x & = &-25\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -25 \\\Leftrightarrow & \color{green}{ x = -25 } & & \\ & V = \left\{ -25 \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-10}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10-7x } & = & -7 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-7}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7-x } & = & -15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &-8x & = &-8\\\Leftrightarrow & \color{red}{-8}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-8}{-8} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+11}& = & -4 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11+13x } & = & -4 \color{red}{ -13x }\color{blue}{-11+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -4 \color{blue}{-11} \\\Leftrightarrow &27x & = &-15\\\Leftrightarrow & \color{red}{27}x & = &-15\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-15}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{-8}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8-x } & = & 2 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &-9x & = &10\\\Leftrightarrow & \color{red}{-9}x & = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-9}& = & 4 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9+7x } & = & 4 \color{red}{ -7x }\color{blue}{+9+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &15x & = &13\\\Leftrightarrow & \color{red}{15}x & = &13\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{13}{15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)