Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-3x+6)& = & 10 \color{red}{-} (12-4x) \\\Leftrightarrow & -9x+18& = &10-12+4x \\\Leftrightarrow & -9x \color{red}{+18} & = &-2 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{+18} \color{blue}{-18} \color{blue}{-4x} & = &-2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-18} \\\Leftrightarrow & -9x-4x& = &-2-18 \\\Leftrightarrow & -13x& = &-20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{20}{13} & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (6x-7)& = & -13 \color{red}{-} (-10-5x) \\\Leftrightarrow & 36x-42& = &-13+10+5x \\\Leftrightarrow & 36x \color{red}{-42} & = &-3 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{-42} \color{blue}{+42} \color{blue}{-5x} & = &-3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+42} \\\Leftrightarrow & 36x-5x& = &-3+42 \\\Leftrightarrow & 31x& = &39 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{39}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{39}{31} & & \\ & V = \left\{ \frac{39}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (6x+1)& = & 10 \color{red}{-} (8-5x) \\\Leftrightarrow & 18x+3& = &10-8+5x \\\Leftrightarrow & 18x \color{red}{+3} & = &2 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+3} \color{blue}{-3} \color{blue}{-5x} & = &2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-3} \\\Leftrightarrow & 18x-5x& = &2-3 \\\Leftrightarrow & 13x& = &-1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-1}{13} & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (2x+3)& = & 3 \color{red}{+} (15-3x) \\\Leftrightarrow & 4x+6& = &3+15-3x \\\Leftrightarrow & 4x \color{red}{+6} & = &18 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+6} \color{blue}{-6} \color{blue}{+3x} & = &18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-6} \\\Leftrightarrow & 4x+3x& = &18-6 \\\Leftrightarrow & 7x& = &12 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{12}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{12}{7} & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (3x-7)& = & 4 \color{red}{-} (-14+x) \\\Leftrightarrow & 18x-42& = &4+14-x \\\Leftrightarrow & 18x \color{red}{-42} & = &18 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 18x+x& = &18+42 \\\Leftrightarrow & 19x& = &60 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{60}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{60}{19} & & \\ & V = \left\{ \frac{60}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x-5)& = & -6 \color{red}{+} (-10-4x) \\\Leftrightarrow & 5x-25& = &-6-10-4x \\\Leftrightarrow & 5x \color{red}{-25} & = &-16 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{-25} \color{blue}{+25} \color{blue}{+4x} & = &-16 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+25} \\\Leftrightarrow & 5x+4x& = &-16+25 \\\Leftrightarrow & 9x& = &9 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{9}{ \color{red}{9} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (4x-1)& = & 11 \color{red}{+} (10-3x) \\\Leftrightarrow & 16x-4& = &11+10-3x \\\Leftrightarrow & 16x \color{red}{-4} & = &21 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &21 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & 16x+3x& = &21+4 \\\Leftrightarrow & 19x& = &25 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{25}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{25}{19} & & \\ & V = \left\{ \frac{25}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (5x+1)& = & 11 \color{red}{-} (14-4x) \\\Leftrightarrow & 25x+5& = &11-14+4x \\\Leftrightarrow & 25x \color{red}{+5} & = &-3 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{+5} \color{blue}{-5} \color{blue}{-4x} & = &-3 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-5} \\\Leftrightarrow & 25x-4x& = &-3-5 \\\Leftrightarrow & 21x& = &-8 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-8}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-8}{21} & & \\ & V = \left\{ \frac{-8}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (2x-3)& = & -10 \color{red}{+} (13-5x) \\\Leftrightarrow & 6x-9& = &-10+13-5x \\\Leftrightarrow & 6x \color{red}{-9} & = &3 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-9} \color{blue}{+9} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+9} \\\Leftrightarrow & 6x+5x& = &3+9 \\\Leftrightarrow & 11x& = &12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (x-2)& = & -15 \color{red}{-} (-10+x) \\\Leftrightarrow & 2x-4& = &-15+10-x \\\Leftrightarrow & 2x \color{red}{-4} & = &-5 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 2x+x& = &-5+4 \\\Leftrightarrow & 3x& = &-1 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-1}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-6x-7)& = & -13 \color{red}{-} (1+x) \\\Leftrightarrow & -30x-35& = &-13-1-x \\\Leftrightarrow & -30x \color{red}{-35} & = &-14 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & -30x+x& = &-14+35 \\\Leftrightarrow & -29x& = &21 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{21}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-21}{29} & & \\ & V = \left\{ \frac{-21}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-4x-4)& = & -10 \color{red}{+} (-3-3x) \\\Leftrightarrow & -16x-16& = &-10-3-3x \\\Leftrightarrow & -16x \color{red}{-16} & = &-13 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &-13 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & -16x+3x& = &-13+16 \\\Leftrightarrow & -13x& = &3 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{3}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)