Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-x } & = & -11 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -11 \color{blue}{+15} \\\Leftrightarrow &-7x & = &4\\\Leftrightarrow & \color{red}{-7}x & = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+2}& = & -5 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2-12x } & = & -5 \color{red}{ +12x }\color{blue}{-2-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & -5 \color{blue}{-2} \\\Leftrightarrow &-x & = &-7\\\Leftrightarrow & \color{red}{-}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-7}{-1} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-14}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14-x } & = & 9 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 9 \color{blue}{+14} \\\Leftrightarrow &-5x & = &23\\\Leftrightarrow & \color{red}{-5}x & = &23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{5} } & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+5}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-x } & = & 5 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 5 \color{blue}{-5} \\\Leftrightarrow &-8x & = &0\\\Leftrightarrow & \color{red}{-8}x & = &0\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{0}{-8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-8}& = & -6 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8+13x } & = & -6 \color{red}{ -13x }\color{blue}{+8+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -6 \color{blue}{+8} \\\Leftrightarrow &27x & = &2\\\Leftrightarrow & \color{red}{27}x & = &2\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{2}{27} \\\Leftrightarrow & \color{green}{ x = \frac{2}{27} } & & \\ & V = \left\{ \frac{2}{27} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-2}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-13x } & = & -7 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -7 \color{blue}{+2} \\\Leftrightarrow &-28x & = &-5\\\Leftrightarrow & \color{red}{-28}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-5}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{5}{28} } & & \\ & V = \left\{ \frac{5}{28} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-11}& = & 10 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11+7x } & = & 10 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &15x & = &21\\\Leftrightarrow & \color{red}{15}x & = &21\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{21}{15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14-x } & = & 7 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 7 \color{blue}{+14} \\\Leftrightarrow &7x & = &21\\\Leftrightarrow & \color{red}{7}x & = &21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{21}{7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+5}& = & -3 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5+9x } & = & -3 \color{red}{ -9x }\color{blue}{-5+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &19x & = &-8\\\Leftrightarrow & \color{red}{19}x & = &-8\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-8}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{19} } & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-1}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 13x \color{red}{-1}\color{blue}{+1-11x } & = & 9 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & 13x \color{blue}{-11x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &2x & = &10\\\Leftrightarrow & \color{red}{2}x & = &10\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{10}{2} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+6}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-5x } & = & 10 \color{red}{ +5x }\color{blue}{-6-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 10 \color{blue}{-6} \\\Leftrightarrow &-14x & = &4\\\Leftrightarrow & \color{red}{-14}x & = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+11}& = & 2 \color{red}{ +11x } \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11-11x } & = & 2 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 7x \color{blue}{-11x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &-4x & = &-9\\\Leftrightarrow & \color{red}{-4}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)