Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & 2x+\frac{3}{4} \\\Leftrightarrow & 9x+\frac{6}{7}& = & 2x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{252}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{56}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 252x \color{red}{+24} & = & \color{red}{56x} +21 \\\Leftrightarrow & 252x \color{red}{+24} \color{blue}{-24} \color{blue}{-56x} & = & \color{red}{56x} +21 \color{blue}{-56x} \color{blue}{-24} \\\Leftrightarrow & 252x-56x& = & 21-24 \\\Leftrightarrow & \color{red}{196} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{196} & & \\ & V = \left\{ \frac{-3}{196} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{2}{3})& = & -9x+\frac{9}{2} \\\Leftrightarrow & 14x-\frac{14}{3}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{-28} & = & \color{red}{-54x} +27 \\\Leftrightarrow & 84x \color{red}{-28} \color{blue}{+28} \color{blue}{+54x} & = & \color{red}{-54x} +27 \color{blue}{+54x} \color{blue}{+28} \\\Leftrightarrow & 84x+54x& = & 27+28 \\\Leftrightarrow & \color{red}{138} x& = & 55 \\\Leftrightarrow & x = \frac{55}{138} & & \\ & V = \left\{ \frac{55}{138} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{5})& = & 7x+\frac{5}{7} \\\Leftrightarrow & 8x-\frac{8}{5}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{56}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-56} & = & \color{red}{245x} +25 \\\Leftrightarrow & 280x \color{red}{-56} \color{blue}{+56} \color{blue}{-245x} & = & \color{red}{245x} +25 \color{blue}{-245x} \color{blue}{+56} \\\Leftrightarrow & 280x-245x& = & 25+56 \\\Leftrightarrow & \color{red}{35} x& = & 81 \\\Leftrightarrow & x = \frac{81}{35} & & \\ & V = \left\{ \frac{81}{35} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{5}{11})& = & 5x+\frac{8}{5} \\\Leftrightarrow & -24x-\frac{30}{11}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x- \frac{150}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{-150} & = & \color{red}{275x} +88 \\\Leftrightarrow & -1320x \color{red}{-150} \color{blue}{+150} \color{blue}{-275x} & = & \color{red}{275x} +88 \color{blue}{-275x} \color{blue}{+150} \\\Leftrightarrow & -1320x-275x& = & 88+150 \\\Leftrightarrow & \color{red}{-1595} x& = & 238 \\\Leftrightarrow & x = \frac{238}{-1595} & & \\\Leftrightarrow & x = \frac{-238}{1595} & & \\ & V = \left\{ \frac{-238}{1595} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{4}{3})& = & 7x+\frac{9}{8} \\\Leftrightarrow & 25x-\frac{20}{3}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{600}{ \color{blue}{24} }x- \frac{160}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{27}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 600x \color{red}{-160} & = & \color{red}{168x} +27 \\\Leftrightarrow & 600x \color{red}{-160} \color{blue}{+160} \color{blue}{-168x} & = & \color{red}{168x} +27 \color{blue}{-168x} \color{blue}{+160} \\\Leftrightarrow & 600x-168x& = & 27+160 \\\Leftrightarrow & \color{red}{432} x& = & 187 \\\Leftrightarrow & x = \frac{187}{432} & & \\ & V = \left\{ \frac{187}{432} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{9})& = & 5x+\frac{2}{9} \\\Leftrightarrow & 12x+\frac{8}{9}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{108}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 108x \color{red}{+8} & = & \color{red}{45x} +2 \\\Leftrightarrow & 108x \color{red}{+8} \color{blue}{-8} \color{blue}{-45x} & = & \color{red}{45x} +2 \color{blue}{-45x} \color{blue}{-8} \\\Leftrightarrow & 108x-45x& = & 2-8 \\\Leftrightarrow & \color{red}{63} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{63} & & \\\Leftrightarrow & x = \frac{-2}{21} & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{5}{9})& = & -8x+\frac{6}{5} \\\Leftrightarrow & -21x-\frac{35}{9}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-945}{ \color{blue}{45} }x- \frac{175}{ \color{blue}{45} })& = & (\frac{-360}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -945x \color{red}{-175} & = & \color{red}{-360x} +54 \\\Leftrightarrow & -945x \color{red}{-175} \color{blue}{+175} \color{blue}{+360x} & = & \color{red}{-360x} +54 \color{blue}{+360x} \color{blue}{+175} \\\Leftrightarrow & -945x+360x& = & 54+175 \\\Leftrightarrow & \color{red}{-585} x& = & 229 \\\Leftrightarrow & x = \frac{229}{-585} & & \\\Leftrightarrow & x = \frac{-229}{585} & & \\ & V = \left\{ \frac{-229}{585} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{11})& = & -9x+\frac{10}{9} \\\Leftrightarrow & -4x-\frac{6}{11}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-396}{ \color{blue}{99} }x- \frac{54}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -396x \color{red}{-54} & = & \color{red}{-891x} +110 \\\Leftrightarrow & -396x \color{red}{-54} \color{blue}{+54} \color{blue}{+891x} & = & \color{red}{-891x} +110 \color{blue}{+891x} \color{blue}{+54} \\\Leftrightarrow & -396x+891x& = & 110+54 \\\Leftrightarrow & \color{red}{495} x& = & 164 \\\Leftrightarrow & x = \frac{164}{495} & & \\ & V = \left\{ \frac{164}{495} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{3}{10})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 9x+\frac{9}{10}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 10 en 7 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{630}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{20}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 630x \color{red}{+63} & = & \color{red}{350x} +20 \\\Leftrightarrow & 630x \color{red}{+63} \color{blue}{-63} \color{blue}{-350x} & = & \color{red}{350x} +20 \color{blue}{-350x} \color{blue}{-63} \\\Leftrightarrow & 630x-350x& = & 20-63 \\\Leftrightarrow & \color{red}{280} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{280} & & \\ & V = \left\{ \frac{-43}{280} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{11})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{30}{11}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{30}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-30} & = & \color{red}{-55x} +6 \\\Leftrightarrow & -132x \color{red}{-30} \color{blue}{+30} \color{blue}{+55x} & = & \color{red}{-55x} +6 \color{blue}{+55x} \color{blue}{+30} \\\Leftrightarrow & -132x+55x& = & 6+30 \\\Leftrightarrow & \color{red}{-77} x& = & 36 \\\Leftrightarrow & x = \frac{36}{-77} & & \\\Leftrightarrow & x = \frac{-36}{77} & & \\ & V = \left\{ \frac{-36}{77} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{4}{7})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -30x-\frac{24}{7}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1890}{ \color{blue}{63} }x- \frac{216}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1890x \color{red}{-216} & = & \color{red}{-441x} +56 \\\Leftrightarrow & -1890x \color{red}{-216} \color{blue}{+216} \color{blue}{+441x} & = & \color{red}{-441x} +56 \color{blue}{+441x} \color{blue}{+216} \\\Leftrightarrow & -1890x+441x& = & 56+216 \\\Leftrightarrow & \color{red}{-1449} x& = & 272 \\\Leftrightarrow & x = \frac{272}{-1449} & & \\\Leftrightarrow & x = \frac{-272}{1449} & & \\ & V = \left\{ \frac{-272}{1449} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{5}{3})& = & -9x+\frac{4}{11} \\\Leftrightarrow & 28x+\frac{35}{3}& = & -9x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x+ \frac{385}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{+385} & = & \color{red}{-297x} +12 \\\Leftrightarrow & 924x \color{red}{+385} \color{blue}{-385} \color{blue}{+297x} & = & \color{red}{-297x} +12 \color{blue}{+297x} \color{blue}{-385} \\\Leftrightarrow & 924x+297x& = & 12-385 \\\Leftrightarrow & \color{red}{1221} x& = & -373 \\\Leftrightarrow & x = \frac{-373}{1221} & & \\ & V = \left\{ \frac{-373}{1221} \right\} & \\\end{align}\)