Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (5x+6)& = & -13 \color{red}{-} (3-2x) \\\Leftrightarrow & 25x+30& = &-13-3+2x \\\Leftrightarrow & 25x \color{red}{+30} & = &-16 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{+30} \color{blue}{-30} \color{blue}{-2x} & = &-16 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-30} \\\Leftrightarrow & 25x-2x& = &-16-30 \\\Leftrightarrow & 23x& = &-46 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-46}{ \color{red}{23} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (5x+5)& = & -11 \color{red}{-} (-14+x) \\\Leftrightarrow & 15x+15& = &-11+14-x \\\Leftrightarrow & 15x \color{red}{+15} & = &3 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 15x+x& = &3-15 \\\Leftrightarrow & 16x& = &-12 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{-12}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{-3}{4} & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-x+2)& = & 4 \color{red}{+} (-7+x) \\\Leftrightarrow & -2x+4& = &4-7+x \\\Leftrightarrow & -2x \color{red}{+4} & = &-3 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -2x-x& = &-3-4 \\\Leftrightarrow & -3x& = &-7 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-7}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{7}{3} & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (5x-6)& = & -5 \color{red}{-} (12+x) \\\Leftrightarrow & 30x-36& = &-5-12-x \\\Leftrightarrow & 30x \color{red}{-36} & = &-17 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 30x+x& = &-17+36 \\\Leftrightarrow & 31x& = &19 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{19}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{19}{31} & & \\ & V = \left\{ \frac{19}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x+6)& = & -1 \color{red}{-} (-12+x) \\\Leftrightarrow & -30x+30& = &-1+12-x \\\Leftrightarrow & -30x \color{red}{+30} & = &11 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -30x+x& = &11-30 \\\Leftrightarrow & -29x& = &-19 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-19}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{19}{29} & & \\ & V = \left\{ \frac{19}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-4x+5)& = & -1 \color{red}{-} (-6+x) \\\Leftrightarrow & -8x+10& = &-1+6-x \\\Leftrightarrow & -8x \color{red}{+10} & = &5 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -8x+x& = &5-10 \\\Leftrightarrow & -7x& = &-5 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-5}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-5x-6)& = & 2 \color{red}{-} (-6+x) \\\Leftrightarrow & -25x-30& = &2+6-x \\\Leftrightarrow & -25x \color{red}{-30} & = &8 \color{red}{-x} \\\Leftrightarrow & -25x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -25x+x& = &8+30 \\\Leftrightarrow & -24x& = &38 \\\Leftrightarrow & \frac{-24x}{ \color{red}{-24} }& = &\frac{38}{ \color{red}{-24} } \\\Leftrightarrow & x = \frac{-19}{12} & & \\ & V = \left\{ \frac{-19}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-4x-6)& = & 12 \color{red}{-} (-7-5x) \\\Leftrightarrow & -16x-24& = &12+7+5x \\\Leftrightarrow & -16x \color{red}{-24} & = &19 \color{red}{+5x} \\\Leftrightarrow & -16x \color{red}{-24} \color{blue}{+24} \color{blue}{-5x} & = &19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+24} \\\Leftrightarrow & -16x-5x& = &19+24 \\\Leftrightarrow & -21x& = &43 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{43}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-43}{21} & & \\ & V = \left\{ \frac{-43}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-5x+7)& = & 12 \color{red}{-} (8+x) \\\Leftrightarrow & -30x+42& = &12-8-x \\\Leftrightarrow & -30x \color{red}{+42} & = &4 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -30x+x& = &4-42 \\\Leftrightarrow & -29x& = &-38 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-38}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{38}{29} & & \\ & V = \left\{ \frac{38}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (3x-3)& = & 9 \color{red}{+} (13-5x) \\\Leftrightarrow & 6x-6& = &9+13-5x \\\Leftrightarrow & 6x \color{red}{-6} & = &22 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &22 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 6x+5x& = &22+6 \\\Leftrightarrow & 11x& = &28 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{28}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{28}{11} & & \\ & V = \left\{ \frac{28}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (5x-5)& = & 5 \color{red}{-} (12+4x) \\\Leftrightarrow & 15x-15& = &5-12-4x \\\Leftrightarrow & 15x \color{red}{-15} & = &-7 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &-7 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & 15x+4x& = &-7+15 \\\Leftrightarrow & 19x& = &8 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{8}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{8}{19} & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (4x+3)& = & 5 \color{red}{+} (-12+3x) \\\Leftrightarrow & 8x+6& = &5-12+3x \\\Leftrightarrow & 8x \color{red}{+6} & = &-7 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & 8x-3x& = &-7-6 \\\Leftrightarrow & 5x& = &-13 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-13}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-13}{5} & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)