Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (5x+4)& = & -12 \color{red}{+} (-1+x) \\\Leftrightarrow & 30x+24& = &-12-1+x \\\Leftrightarrow & 30x \color{red}{+24} & = &-13 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 30x-x& = &-13-24 \\\Leftrightarrow & 29x& = &-37 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-37}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-37}{29} & & \\ & V = \left\{ \frac{-37}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (4x+7)& = & -9 \color{red}{-} (1+x) \\\Leftrightarrow & 24x+42& = &-9-1-x \\\Leftrightarrow & 24x \color{red}{+42} & = &-10 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 24x+x& = &-10-42 \\\Leftrightarrow & 25x& = &-52 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-52}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-52}{25} & & \\ & V = \left\{ \frac{-52}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x+5)& = & 1 \color{red}{-} (-4-2x) \\\Leftrightarrow & 25x+25& = &1+4+2x \\\Leftrightarrow & 25x \color{red}{+25} & = &5 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{+25} \color{blue}{-25} \color{blue}{-2x} & = &5 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-25} \\\Leftrightarrow & 25x-2x& = &5-25 \\\Leftrightarrow & 23x& = &-20 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-20}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-20}{23} & & \\ & V = \left\{ \frac{-20}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (x-1)& = & -9 \color{red}{-} (-12-5x) \\\Leftrightarrow & 6x-6& = &-9+12+5x \\\Leftrightarrow & 6x \color{red}{-6} & = &3 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 6x-5x& = &3+6 \\\Leftrightarrow & x& = &9 \\ & V = \left\{ 9 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x+3)& = & -7 \color{red}{+} (-7+x) \\\Leftrightarrow & 36x+18& = &-7-7+x \\\Leftrightarrow & 36x \color{red}{+18} & = &-14 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 36x-x& = &-14-18 \\\Leftrightarrow & 35x& = &-32 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-32}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-32}{35} & & \\ & V = \left\{ \frac{-32}{35} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-x+6)& = & -10 \color{red}{+} (12-5x) \\\Leftrightarrow & -6x+36& = &-10+12-5x \\\Leftrightarrow & -6x \color{red}{+36} & = &2 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & -6x+5x& = &2-36 \\\Leftrightarrow & -x& = &-34 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-34}{ \color{red}{-1} } \\\Leftrightarrow & x = 34 & & \\ & V = \left\{ 34 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-6x-7)& = & 5 \color{red}{+} (11-5x) \\\Leftrightarrow & -18x-21& = &5+11-5x \\\Leftrightarrow & -18x \color{red}{-21} & = &16 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-21} \color{blue}{+21} \color{blue}{+5x} & = &16 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+21} \\\Leftrightarrow & -18x+5x& = &16+21 \\\Leftrightarrow & -13x& = &37 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{37}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-37}{13} & & \\ & V = \left\{ \frac{-37}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-3x+7)& = & -2 \color{red}{-} (15+x) \\\Leftrightarrow & -18x+42& = &-2-15-x \\\Leftrightarrow & -18x \color{red}{+42} & = &-17 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -18x+x& = &-17-42 \\\Leftrightarrow & -17x& = &-59 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-59}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{59}{17} & & \\ & V = \left\{ \frac{59}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-3x+1)& = & 14 \color{red}{-} (10+x) \\\Leftrightarrow & -6x+2& = &14-10-x \\\Leftrightarrow & -6x \color{red}{+2} & = &4 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -6x+x& = &4-2 \\\Leftrightarrow & -5x& = &2 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{2}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-3x-2)& = & 4 \color{red}{+} (13-5x) \\\Leftrightarrow & -18x-12& = &4+13-5x \\\Leftrightarrow & -18x \color{red}{-12} & = &17 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -18x+5x& = &17+12 \\\Leftrightarrow & -13x& = &29 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{29}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-29}{13} & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (5x+5)& = & 15 \color{red}{-} (-7+x) \\\Leftrightarrow & 30x+30& = &15+7-x \\\Leftrightarrow & 30x \color{red}{+30} & = &22 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 30x+x& = &22-30 \\\Leftrightarrow & 31x& = &-8 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-8}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-8}{31} & & \\ & V = \left\{ \frac{-8}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-x-3)& = & -8 \color{red}{+} (7+x) \\\Leftrightarrow & -5x-15& = &-8+7+x \\\Leftrightarrow & -5x \color{red}{-15} & = &-1 \color{red}{+x} \\\Leftrightarrow & -5x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -5x-x& = &-1+15 \\\Leftrightarrow & -6x& = &14 \\\Leftrightarrow & \frac{-6x}{ \color{red}{-6} }& = &\frac{14}{ \color{red}{-6} } \\\Leftrightarrow & x = \frac{-7}{3} & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)