Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+11}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11-x } & = & 12 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 12 \color{blue}{-11} \\\Leftrightarrow &7x & = &1\\\Leftrightarrow & \color{red}{7}x & = &1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+6}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6-x } & = & 3 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 3 \color{blue}{-6} \\\Leftrightarrow &-12x & = &-3\\\Leftrightarrow & \color{red}{-12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+11}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-x } & = & -6 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -6 \color{blue}{-11} \\\Leftrightarrow &-14x & = &-17\\\Leftrightarrow & \color{red}{-14}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-17}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{17}{14} } & & \\ & V = \left\{ \frac{17}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+5}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-x } & = & 14 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &-10x & = &9\\\Leftrightarrow & \color{red}{-10}x & = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-1}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{-1}\color{blue}{+1-13x } & = & 15 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &-15x & = &16\\\Leftrightarrow & \color{red}{-15}x & = &16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{15} } & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-14}& = & -5 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14-8x } & = & -5 \color{red}{ +8x }\color{blue}{+14-8x } \\\Leftrightarrow & 15x \color{blue}{-8x } & = & -5 \color{blue}{+14} \\\Leftrightarrow &7x & = &9\\\Leftrightarrow & \color{red}{7}x & = &9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-3}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3-4x } & = & -1 \color{red}{ +4x }\color{blue}{+3-4x } \\\Leftrightarrow & 5x \color{blue}{-4x } & = & -1 \color{blue}{+3} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+7}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7-7x } & = & 1 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & x \color{blue}{-7x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &-6x & = &-6\\\Leftrightarrow & \color{red}{-6}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-6}{-6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{+8}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8-x } & = & 7 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 7 \color{blue}{-8} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+12}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-5x } & = & 11 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &-7x & = &-1\\\Leftrightarrow & \color{red}{-7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+9}& = & -7 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9-4x } & = & -7 \color{red}{ +4x }\color{blue}{-9-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & -7 \color{blue}{-9} \\\Leftrightarrow &11x & = &-16\\\Leftrightarrow & \color{red}{11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+14}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14-x } & = & -4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &-6x & = &-18\\\Leftrightarrow & \color{red}{-6}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-18}{-6} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)