Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-2}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-x } & = & 6 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 6 \color{blue}{+2} \\\Leftrightarrow &-12x & = &8\\\Leftrightarrow & \color{red}{-12}x & = &8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+5}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5+13x } & = & -3 \color{red}{ -13x }\color{blue}{-5+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &22x & = &-8\\\Leftrightarrow & \color{red}{22}x & = &-8\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-8}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-15}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-13x } & = & 5 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 5 \color{blue}{+15} \\\Leftrightarrow &-28x & = &20\\\Leftrightarrow & \color{red}{-28}x & = &20\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{20}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-13}& = & -11 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13-10x } & = & -11 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & 11x \color{blue}{-10x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-3}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-x } & = & 1 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 1 \color{blue}{+3} \\\Leftrightarrow &11x & = &4\\\Leftrightarrow & \color{red}{11}x & = &4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-5}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{-5}\color{blue}{+5-5x } & = & -4 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & -4 \color{blue}{+5} \\\Leftrightarrow &8x & = &1\\\Leftrightarrow & \color{red}{8}x & = &1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+14}& = & -3 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14+12x } & = & -3 \color{red}{ -12x }\color{blue}{-14+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &25x & = &-17\\\Leftrightarrow & \color{red}{25}x & = &-17\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-17}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{25} } & & \\ & V = \left\{ \frac{-17}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+10}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+10}\color{blue}{-10-11x } & = & 7 \color{red}{ +11x }\color{blue}{-10-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 7 \color{blue}{-10} \\\Leftrightarrow &-3x & = &-3\\\Leftrightarrow & \color{red}{-3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+10}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10-5x } & = & 12 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 12 \color{blue}{-10} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{-8}& = & 5 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8-2x } & = & 5 \color{red}{ +2x }\color{blue}{+8-2x } \\\Leftrightarrow & 15x \color{blue}{-2x } & = & 5 \color{blue}{+8} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-9}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-13x } & = & -13 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &-16x & = &-4\\\Leftrightarrow & \color{red}{-16}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+1}& = & 12 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+1}\color{blue}{-1+13x } & = & 12 \color{red}{ -13x }\color{blue}{-1+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &27x & = &11\\\Leftrightarrow & \color{red}{27}x & = &11\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{11}{27} \\\Leftrightarrow & \color{green}{ x = \frac{11}{27} } & & \\ & V = \left\{ \frac{11}{27} \right\} & \\\end{align}\)