Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-3}& = & -10 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-3}\color{blue}{+3-4x } & = & -10 \color{red}{ +4x }\color{blue}{+3-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &-19x & = &-7\\\Leftrightarrow & \color{red}{-19}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-7}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-15}& = & 14 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15-2x } & = & 14 \color{red}{ +2x }\color{blue}{+15-2x } \\\Leftrightarrow & 7x \color{blue}{-2x } & = & 14 \color{blue}{+15} \\\Leftrightarrow &5x & = &29\\\Leftrightarrow & \color{red}{5}x & = &29\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{29}{5} \\\Leftrightarrow & \color{green}{ x = \frac{29}{5} } & & \\ & V = \left\{ \frac{29}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-15}\color{blue}{+15-x } & = & -2 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &-4x & = &13\\\Leftrightarrow & \color{red}{-4}x & = &13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{4} } & & \\ & V = \left\{ \frac{-13}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+14}& = & -2 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14+6x } & = & -2 \color{red}{ -6x }\color{blue}{-14+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -2 \color{blue}{-14} \\\Leftrightarrow &19x & = &-16\\\Leftrightarrow & \color{red}{19}x & = &-16\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-16}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{19} } & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-11}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-x } & = & 12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &-9x & = &23\\\Leftrightarrow & \color{red}{-9}x & = &23\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{23}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{9} } & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-7}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7-7x } & = & -15 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &3x & = &-8\\\Leftrightarrow & \color{red}{3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{-14}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x } & = & 10 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{+14} \\\Leftrightarrow &-15x & = &24\\\Leftrightarrow & \color{red}{-15}x & = &24\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{24}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-15}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-7x } & = & -7 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &-20x & = &8\\\Leftrightarrow & \color{red}{-20}x & = &8\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{8}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+8}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-x } & = & -10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -10 \color{blue}{-8} \\\Leftrightarrow &-9x & = &-18\\\Leftrightarrow & \color{red}{-9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-18}{-9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-5}& = & -3 \color{red}{ +2x } \\\Leftrightarrow & 3x \color{red}{-5}\color{blue}{+5-2x } & = & -3 \color{red}{ +2x }\color{blue}{+5-2x } \\\Leftrightarrow & 3x \color{blue}{-2x } & = & -3 \color{blue}{+5} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-x } & = & 13 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 13 \color{blue}{-5} \\\Leftrightarrow &-12x & = &8\\\Leftrightarrow & \color{red}{-12}x & = &8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+7}& = & 12 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-12x } & = & 12 \color{red}{ +12x }\color{blue}{-7-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 12 \color{blue}{-7} \\\Leftrightarrow &-23x & = &5\\\Leftrightarrow & \color{red}{-23}x & = &5\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{5}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{23} } & & \\ & V = \left\{ \frac{-5}{23} \right\} & \\\end{align}\)