Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-7}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7-5x } & = & -8 \color{red}{ +5x }\color{blue}{+7-5x } \\\Leftrightarrow & 3x \color{blue}{-5x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &-2x & = &-1\\\Leftrightarrow & \color{red}{-2}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-1}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+12}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12-x } & = & 4 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 4 \color{blue}{-12} \\\Leftrightarrow &-10x & = &-8\\\Leftrightarrow & \color{red}{-10}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+12}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12-x } & = & -6 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -6 \color{blue}{-12} \\\Leftrightarrow &-7x & = &-18\\\Leftrightarrow & \color{red}{-7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-11}& = & 7 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{-11}\color{blue}{+11-4x } & = & 7 \color{red}{ +4x }\color{blue}{+11-4x } \\\Leftrightarrow & 13x \color{blue}{-4x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &9x & = &18\\\Leftrightarrow & \color{red}{9}x & = &18\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{18}{9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+10}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10-7x } & = & 3 \color{red}{ +7x }\color{blue}{-10-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+11}& = & 8 \color{red}{ -5x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11+5x } & = & 8 \color{red}{ -5x }\color{blue}{-11+5x } \\\Leftrightarrow & -x \color{blue}{+5x } & = & 8 \color{blue}{-11} \\\Leftrightarrow &4x & = &-3\\\Leftrightarrow & \color{red}{4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+1}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1-x } & = & 11 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 11 \color{blue}{-1} \\\Leftrightarrow &4x & = &10\\\Leftrightarrow & \color{red}{4}x & = &10\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{10}{4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+10}& = & -3 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10-2x } & = & -3 \color{red}{ +2x }\color{blue}{-10-2x } \\\Leftrightarrow & 7x \color{blue}{-2x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &5x & = &-13\\\Leftrightarrow & \color{red}{5}x & = &-13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+14}& = & 14 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14-8x } & = & 14 \color{red}{ +8x }\color{blue}{-14-8x } \\\Leftrightarrow & 15x \color{blue}{-8x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+13}\color{blue}{-13-x } & = & -1 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -1 \color{blue}{-13} \\\Leftrightarrow &-16x & = &-14\\\Leftrightarrow & \color{red}{-16}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+4}& = & 15 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4+6x } & = & 15 \color{red}{ -6x }\color{blue}{-4+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 15 \color{blue}{-4} \\\Leftrightarrow &19x & = &11\\\Leftrightarrow & \color{red}{19}x & = &11\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{11}{19} \\\Leftrightarrow & \color{green}{ x = \frac{11}{19} } & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-12}& = & 1 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-3x } & = & 1 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 1 \color{blue}{+12} \\\Leftrightarrow &-8x & = &13\\\Leftrightarrow & \color{red}{-8}x & = &13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)