Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-14}& = & 4 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{-14}\color{blue}{+14+9x } & = & 4 \color{red}{ -9x }\color{blue}{+14+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & 4 \color{blue}{+14} \\\Leftrightarrow &8x & = &18\\\Leftrightarrow & \color{red}{8}x & = &18\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{18}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-5}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-5}\color{blue}{+5-13x } & = & -1 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &-16x & = &4\\\Leftrightarrow & \color{red}{-16}x & = &4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+9}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-x } & = & 7 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 7 \color{blue}{-9} \\\Leftrightarrow &-14x & = &-2\\\Leftrightarrow & \color{red}{-14}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-2}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-x } & = & -6 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -6 \color{blue}{+2} \\\Leftrightarrow &-16x & = &-4\\\Leftrightarrow & \color{red}{-16}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-3}& = & 15 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3-12x } & = & 15 \color{red}{ +12x }\color{blue}{+3-12x } \\\Leftrightarrow & 13x \color{blue}{-12x } & = & 15 \color{blue}{+3} \\\Leftrightarrow &x & = &18\\\Leftrightarrow & \color{red}{}x & = &18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 18 \\\Leftrightarrow & \color{green}{ x = 18 } & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-10}& = & -2 \color{red}{ -15x } \\\Leftrightarrow & x \color{red}{-10}\color{blue}{+10+15x } & = & -2 \color{red}{ -15x }\color{blue}{+10+15x } \\\Leftrightarrow & x \color{blue}{+15x } & = & -2 \color{blue}{+10} \\\Leftrightarrow &16x & = &8\\\Leftrightarrow & \color{red}{16}x & = &8\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{8}{16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+2}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-13x } & = & -8 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -8 \color{blue}{-2} \\\Leftrightarrow &-16x & = &-10\\\Leftrightarrow & \color{red}{-16}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-1}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1-x } & = & 7 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &-14x & = &8\\\Leftrightarrow & \color{red}{-14}x & = &8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+3}\color{blue}{-3-x } & = & -11 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -11 \color{blue}{-3} \\\Leftrightarrow &-16x & = &-14\\\Leftrightarrow & \color{red}{-16}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-12}& = & 15 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12-10x } & = & 15 \color{red}{ +10x }\color{blue}{+12-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & 15 \color{blue}{+12} \\\Leftrightarrow &-x & = &27\\\Leftrightarrow & \color{red}{-}x & = &27\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{27}{-1} \\\Leftrightarrow & \color{green}{ x = -27 } & & \\ & V = \left\{ -27 \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-5}& = & 10 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-5}\color{blue}{+5+9x } & = & 10 \color{red}{ -9x }\color{blue}{+5+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & 10 \color{blue}{+5} \\\Leftrightarrow &23x & = &15\\\Leftrightarrow & \color{red}{23}x & = &15\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{15}{23} \\\Leftrightarrow & \color{green}{ x = \frac{15}{23} } & & \\ & V = \left\{ \frac{15}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-5}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-x } & = & 10 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 10 \color{blue}{+5} \\\Leftrightarrow &x & = &15\\\Leftrightarrow & \color{red}{}x & = &15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 15 \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)