Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+13}& = & -2 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13+2x } & = & -2 \color{red}{ -2x }\color{blue}{-13+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -2 \color{blue}{-13} \\\Leftrightarrow &5x & = &-15\\\Leftrightarrow & \color{red}{5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-15}{5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-7}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-7}\color{blue}{+7-9x } & = & 5 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 5 \color{blue}{+7} \\\Leftrightarrow &-17x & = &12\\\Leftrightarrow & \color{red}{-17}x & = &12\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{12}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{17} } & & \\ & V = \left\{ \frac{-12}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+5}& = & -15 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5+11x } & = & -15 \color{red}{ -11x }\color{blue}{-5+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &14x & = &-20\\\Leftrightarrow & \color{red}{14}x & = &-20\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-20}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+15}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15-7x } & = & 11 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 11 \color{blue}{-15} \\\Leftrightarrow &-17x & = &-4\\\Leftrightarrow & \color{red}{-17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+14}& = & -4 \color{red}{ +12x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-12x } & = & -4 \color{red}{ +12x }\color{blue}{-14-12x } \\\Leftrightarrow & -7x \color{blue}{-12x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &-19x & = &-18\\\Leftrightarrow & \color{red}{-19}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-18}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{18}{19} } & & \\ & V = \left\{ \frac{18}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+8}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-x } & = & 5 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &-14x & = &-3\\\Leftrightarrow & \color{red}{-14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+8}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-x } & = & -8 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -8 \color{blue}{-8} \\\Leftrightarrow &-4x & = &-16\\\Leftrightarrow & \color{red}{-4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-16}{-4} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+4}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4-7x } & = & -13 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & -13 \color{blue}{-4} \\\Leftrightarrow &5x & = &-17\\\Leftrightarrow & \color{red}{5}x & = &-17\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-17}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{5} } & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11-x } & = & -8 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -8 \color{blue}{+11} \\\Leftrightarrow &2x & = &3\\\Leftrightarrow & \color{red}{2}x & = &3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+1}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-x } & = & 6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &-12x & = &5\\\Leftrightarrow & \color{red}{-12}x & = &5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-12}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-x } & = & 1 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 1 \color{blue}{+12} \\\Leftrightarrow &-3x & = &13\\\Leftrightarrow & \color{red}{-3}x & = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{-4}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4-11x } & = & 1 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & 1 \color{blue}{+4} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)