Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+11}& = & 1 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11+6x } & = & 1 \color{red}{ -6x }\color{blue}{-11+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 1 \color{blue}{-11} \\\Leftrightarrow &19x & = &-10\\\Leftrightarrow & \color{red}{19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+14}& = & 3 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+14}\color{blue}{-14+7x } & = & 3 \color{red}{ -7x }\color{blue}{-14+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &12x & = &-11\\\Leftrightarrow & \color{red}{12}x & = &-11\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-11}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{12} } & & \\ & V = \left\{ \frac{-11}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+14}& = & 14 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14+7x } & = & 14 \color{red}{ -7x }\color{blue}{-14+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &15x & = &0\\\Leftrightarrow & \color{red}{15}x & = &0\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{0}{15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-x } & = & -8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &-11x & = &-12\\\Leftrightarrow & \color{red}{-11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-12}& = & -1 \color{red}{ -3x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12+3x } & = & -1 \color{red}{ -3x }\color{blue}{+12+3x } \\\Leftrightarrow & -x \color{blue}{+3x } & = & -1 \color{blue}{+12} \\\Leftrightarrow &2x & = &11\\\Leftrightarrow & \color{red}{2}x & = &11\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{11}{2} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+3}& = & 3 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3+5x } & = & 3 \color{red}{ -5x }\color{blue}{-3+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-8}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8-13x } & = & 7 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & 7 \color{blue}{+8} \\\Leftrightarrow &-9x & = &15\\\Leftrightarrow & \color{red}{-9}x & = &15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-7}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-11x } & = & 10 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & -13x \color{blue}{-11x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &-24x & = &17\\\Leftrightarrow & \color{red}{-24}x & = &17\\\Leftrightarrow & \frac{\color{red}{-24}x}{ \color{blue}{ -24}} & = & \frac{17}{-24} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{24} } & & \\ & V = \left\{ \frac{-17}{24} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-4}& = & 7 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4+5x } & = & 7 \color{red}{ -5x }\color{blue}{+4+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 7 \color{blue}{+4} \\\Leftrightarrow &11x & = &11\\\Leftrightarrow & \color{red}{11}x & = &11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{11}{11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-2}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2-x } & = & -15 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -15 \color{blue}{+2} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+9}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-x } & = & -2 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+3}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3-x } & = & 6 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 6 \color{blue}{-3} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)