Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-7x-13=14+x\)
2. \(-3x+5=4+10x\)
3. \(-8x-1=12+x\)
4. \(13x+2=4-6x\)
5. \(-x+12=4+0x\)
6. \(-x-6=1+12x\)
7. \(-2x+12=7+x\)
8. \(13x+9=-15+8x\)
9. \(-6x-9=6+x\)
10. \(10x-14=-7-3x\)
11. \(-15x-4=8+x\)
12. \(11x+13=-13-10x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-13}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-x } & = & 14 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 14 \color{blue}{+13} \\\Leftrightarrow &-8x & = &27\\\Leftrightarrow & \color{red}{-8}x & = &27\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{27}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{8} } & & \\ & V = \left\{ \frac{-27}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+5}& = & 4 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-10x } & = & 4 \color{red}{ +10x }\color{blue}{-5-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-1}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-x } & = & 12 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 12 \color{blue}{+1} \\\Leftrightarrow &-9x & = &13\\\Leftrightarrow & \color{red}{-9}x & = &13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+2}& = & 4 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2+6x } & = & 4 \color{red}{ -6x }\color{blue}{-2+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &19x & = &2\\\Leftrightarrow & \color{red}{19}x & = &2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{2}{19} } & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+12}& = & 4 \color{red}{ +0x } \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12+0x } & = & 4 \color{red}{ +0x }\color{blue}{-12+0x } \\\Leftrightarrow & -x \color{blue}{+0x } & = & 4 \color{blue}{-12} \\\Leftrightarrow &-x & = &-8\\\Leftrightarrow & \color{red}{-}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-8}{-1} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-6}& = & 1 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6-12x } & = & 1 \color{red}{ +12x }\color{blue}{+6-12x } \\\Leftrightarrow & -x \color{blue}{-12x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &-13x & = &7\\\Leftrightarrow & \color{red}{-13}x & = &7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-x } & = & 7 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 7 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-5\\\Leftrightarrow & \color{red}{-3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+9}& = & -15 \color{red}{ +8x } \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9-8x } & = & -15 \color{red}{ +8x }\color{blue}{-9-8x } \\\Leftrightarrow & 13x \color{blue}{-8x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &5x & = &-24\\\Leftrightarrow & \color{red}{5}x & = &-24\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-24}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{5} } & & \\ & V = \left\{ \frac{-24}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-9}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9-x } & = & 6 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &-7x & = &15\\\Leftrightarrow & \color{red}{-7}x & = &15\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{15}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-14}& = & -7 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14+3x } & = & -7 \color{red}{ -3x }\color{blue}{+14+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &13x & = &7\\\Leftrightarrow & \color{red}{13}x & = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-4}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4-x } & = & 8 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &-16x & = &12\\\Leftrightarrow & \color{red}{-16}x & = &12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+13}& = & -13 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13+10x } & = & -13 \color{red}{ -10x }\color{blue}{-13+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & -13 \color{blue}{-13} \\\Leftrightarrow &21x & = &-26\\\Leftrightarrow & \color{red}{21}x & = &-26\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-26}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{21} } & & \\ & V = \left\{ \frac{-26}{21} \right\} & \\\end{align}\)