Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+4}& = & -6 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-4x } & = & -6 \color{red}{ +4x }\color{blue}{-4-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &-11x & = &-10\\\Leftrightarrow & \color{red}{-11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+13}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13-5x } & = & 11 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 11 \color{blue}{-13} \\\Leftrightarrow &7x & = &-2\\\Leftrightarrow & \color{red}{7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+3}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-x } & = & -15 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -15 \color{blue}{-3} \\\Leftrightarrow &-12x & = &-18\\\Leftrightarrow & \color{red}{-12}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-18}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+7}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7-x } & = & -9 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -9 \color{blue}{-7} \\\Leftrightarrow &-5x & = &-16\\\Leftrightarrow & \color{red}{-5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-5}& = & 13 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-5}\color{blue}{+5+7x } & = & 13 \color{red}{ -7x }\color{blue}{+5+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &19x & = &18\\\Leftrightarrow & \color{red}{19}x & = &18\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{18}{19} \\\Leftrightarrow & \color{green}{ x = \frac{18}{19} } & & \\ & V = \left\{ \frac{18}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+7}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7+11x } & = & 4 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 4 \color{blue}{-7} \\\Leftrightarrow &20x & = &-3\\\Leftrightarrow & \color{red}{20}x & = &-3\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-3}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{20} } & & \\ & V = \left\{ \frac{-3}{20} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-9}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-x } & = & -11 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -11 \color{blue}{+9} \\\Leftrightarrow &-10x & = &-2\\\Leftrightarrow & \color{red}{-10}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+11}& = & 10 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11-6x } & = & 10 \color{red}{ +6x }\color{blue}{-11-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 10 \color{blue}{-11} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-15}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-x } & = & -13 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -13 \color{blue}{+15} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+15}& = & -2 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-10x } & = & -2 \color{red}{ +10x }\color{blue}{-15-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & -2 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-17\\\Leftrightarrow & \color{red}{-13}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{17}{13} } & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+12}& = & -10 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12-11x } & = & -10 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -10 \color{blue}{-12} \\\Leftrightarrow &-6x & = &-22\\\Leftrightarrow & \color{red}{-6}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-22}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+12}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12-11x } & = & -11 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -11 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-23\\\Leftrightarrow & \color{red}{-5}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{23}{5} } & & \\ & V = \left\{ \frac{23}{5} \right\} & \\\end{align}\)