Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+7}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+7}\color{blue}{-7-x } & = & 5 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 5 \color{blue}{-7} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+13}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+13}\color{blue}{-13-x } & = & -9 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -9 \color{blue}{-13} \\\Leftrightarrow &-5x & = &-22\\\Leftrightarrow & \color{red}{-5}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-22}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{22}{5} } & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{+4}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-11x } & = & -8 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &-18x & = &-12\\\Leftrightarrow & \color{red}{-18}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-12}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+10}\color{blue}{-10-x } & = & -13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &-14x & = &-23\\\Leftrightarrow & \color{red}{-14}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-23}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{23}{14} } & & \\ & V = \left\{ \frac{23}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-7}& = & 5 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-8x } & = & 5 \color{red}{ +8x }\color{blue}{+7-8x } \\\Leftrightarrow & -13x \color{blue}{-8x } & = & 5 \color{blue}{+7} \\\Leftrightarrow &-21x & = &12\\\Leftrightarrow & \color{red}{-21}x & = &12\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{12}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-x } & = & 3 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 3 \color{blue}{-11} \\\Leftrightarrow &-16x & = &-8\\\Leftrightarrow & \color{red}{-16}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-15}& = & -9 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15-2x } & = & -9 \color{red}{ +2x }\color{blue}{+15-2x } \\\Leftrightarrow & 9x \color{blue}{-2x } & = & -9 \color{blue}{+15} \\\Leftrightarrow &7x & = &6\\\Leftrightarrow & \color{red}{7}x & = &6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+12}& = & -13 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{+12}\color{blue}{-12+2x } & = & -13 \color{red}{ -2x }\color{blue}{-12+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & -13 \color{blue}{-12} \\\Leftrightarrow &3x & = &-25\\\Leftrightarrow & \color{red}{3}x & = &-25\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-25}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{3} } & & \\ & V = \left\{ \frac{-25}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+9}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-x } & = & 12 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 12 \color{blue}{-9} \\\Leftrightarrow &-16x & = &3\\\Leftrightarrow & \color{red}{-16}x & = &3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{16} } & & \\ & V = \left\{ \frac{-3}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{-4}& = & 15 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4+7x } & = & 15 \color{red}{ -7x }\color{blue}{+4+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 15 \color{blue}{+4} \\\Leftrightarrow &22x & = &19\\\Leftrightarrow & \color{red}{22}x & = &19\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{19}{22} \\\Leftrightarrow & \color{green}{ x = \frac{19}{22} } & & \\ & V = \left\{ \frac{19}{22} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+6}& = & -6 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-4x } & = & -6 \color{red}{ +4x }\color{blue}{-6-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -6 \color{blue}{-6} \\\Leftrightarrow &-19x & = &-12\\\Leftrightarrow & \color{red}{-19}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-12}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{12}{19} } & & \\ & V = \left\{ \frac{12}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{-13}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{-13}\color{blue}{+13-7x } & = & -9 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & -9 \color{blue}{+13} \\\Leftrightarrow &-9x & = &4\\\Leftrightarrow & \color{red}{-9}x & = &4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)