Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+1}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+1}\color{blue}{-1-9x } & = & 6 \color{red}{ +9x }\color{blue}{-1-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &5x & = &5\\\Leftrightarrow & \color{red}{5}x & = &5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{5}{5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+11}& = & -2 \color{red}{ -6x } \\\Leftrightarrow & x \color{red}{+11}\color{blue}{-11+6x } & = & -2 \color{red}{ -6x }\color{blue}{-11+6x } \\\Leftrightarrow & x \color{blue}{+6x } & = & -2 \color{blue}{-11} \\\Leftrightarrow &7x & = &-13\\\Leftrightarrow & \color{red}{7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-4}& = & 6 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4-4x } & = & 6 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 6 \color{blue}{+4} \\\Leftrightarrow &-19x & = &10\\\Leftrightarrow & \color{red}{-19}x & = &10\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{10}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+4}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+4}\color{blue}{-4+11x } & = & -3 \color{red}{ -11x }\color{blue}{-4+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &15x & = &-7\\\Leftrightarrow & \color{red}{15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4-x } & = & 5 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 5 \color{blue}{-4} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-6}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6-11x } & = & -3 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+6}& = & -5 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6-2x } & = & -5 \color{red}{ +2x }\color{blue}{-6-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & -5 \color{blue}{-6} \\\Leftrightarrow &-3x & = &-11\\\Leftrightarrow & \color{red}{-3}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-x } & = & 13 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 13 \color{blue}{-5} \\\Leftrightarrow &-12x & = &8\\\Leftrightarrow & \color{red}{-12}x & = &8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x } & = & -9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -9 \color{blue}{+10} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-12}& = & -10 \color{red}{ +14x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12-14x } & = & -10 \color{red}{ +14x }\color{blue}{+12-14x } \\\Leftrightarrow & 3x \color{blue}{-14x } & = & -10 \color{blue}{+12} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-11}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-11}\color{blue}{+11-13x } & = & 13 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &-25x & = &24\\\Leftrightarrow & \color{red}{-25}x & = &24\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{24}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{25} } & & \\ & V = \left\{ \frac{-24}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+2}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2-7x } & = & 10 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & -x \color{blue}{-7x } & = & 10 \color{blue}{-2} \\\Leftrightarrow &-8x & = &8\\\Leftrightarrow & \color{red}{-8}x & = &8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{8}{-8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)