Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{4}{3})& = & -3x+\frac{10}{11} \\\Leftrightarrow & 20x-\frac{20}{3}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-220} & = & \color{red}{-99x} +30 \\\Leftrightarrow & 660x \color{red}{-220} \color{blue}{+220} \color{blue}{+99x} & = & \color{red}{-99x} +30 \color{blue}{+99x} \color{blue}{+220} \\\Leftrightarrow & 660x+99x& = & 30+220 \\\Leftrightarrow & \color{red}{759} x& = & 250 \\\Leftrightarrow & x = \frac{250}{759} & & \\ & V = \left\{ \frac{250}{759} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{4}{9})& = & -3x+\frac{3}{2} \\\Leftrightarrow & -28x-\frac{28}{9}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-504}{ \color{blue}{18} }x- \frac{56}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -504x \color{red}{-56} & = & \color{red}{-54x} +27 \\\Leftrightarrow & -504x \color{red}{-56} \color{blue}{+56} \color{blue}{+54x} & = & \color{red}{-54x} +27 \color{blue}{+54x} \color{blue}{+56} \\\Leftrightarrow & -504x+54x& = & 27+56 \\\Leftrightarrow & \color{red}{-450} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-450} & & \\\Leftrightarrow & x = \frac{-83}{450} & & \\ & V = \left\{ \frac{-83}{450} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{3}{8})& = & -6x+\frac{10}{9} \\\Leftrightarrow & -35x-\frac{21}{8}& = & -6x+\frac{10}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-2520}{ \color{blue}{72} }x- \frac{189}{ \color{blue}{72} })& = & (\frac{-432}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -2520x \color{red}{-189} & = & \color{red}{-432x} +80 \\\Leftrightarrow & -2520x \color{red}{-189} \color{blue}{+189} \color{blue}{+432x} & = & \color{red}{-432x} +80 \color{blue}{+432x} \color{blue}{+189} \\\Leftrightarrow & -2520x+432x& = & 80+189 \\\Leftrightarrow & \color{red}{-2088} x& = & 269 \\\Leftrightarrow & x = \frac{269}{-2088} & & \\\Leftrightarrow & x = \frac{-269}{2088} & & \\ & V = \left\{ \frac{-269}{2088} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{5})& = & -2x+\frac{9}{2} \\\Leftrightarrow & -18x-\frac{18}{5}& = & -2x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-180}{ \color{blue}{10} }x- \frac{36}{ \color{blue}{10} })& = & (\frac{-20}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{-20x} +45 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{+20x} & = & \color{red}{-20x} +45 \color{blue}{+20x} \color{blue}{+36} \\\Leftrightarrow & -180x+20x& = & 45+36 \\\Leftrightarrow & \color{red}{-160} x& = & 81 \\\Leftrightarrow & x = \frac{81}{-160} & & \\\Leftrightarrow & x = \frac{-81}{160} & & \\ & V = \left\{ \frac{-81}{160} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & -2x+\frac{4}{3} \\\Leftrightarrow & 21x-\frac{21}{8}& = & -2x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{504}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{-48}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 504x \color{red}{-63} & = & \color{red}{-48x} +32 \\\Leftrightarrow & 504x \color{red}{-63} \color{blue}{+63} \color{blue}{+48x} & = & \color{red}{-48x} +32 \color{blue}{+48x} \color{blue}{+63} \\\Leftrightarrow & 504x+48x& = & 32+63 \\\Leftrightarrow & \color{red}{552} x& = & 95 \\\Leftrightarrow & x = \frac{95}{552} & & \\ & V = \left\{ \frac{95}{552} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{4}{5})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -30x-\frac{24}{5}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1350}{ \color{blue}{45} }x- \frac{216}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1350x \color{red}{-216} & = & \color{red}{-315x} +20 \\\Leftrightarrow & -1350x \color{red}{-216} \color{blue}{+216} \color{blue}{+315x} & = & \color{red}{-315x} +20 \color{blue}{+315x} \color{blue}{+216} \\\Leftrightarrow & -1350x+315x& = & 20+216 \\\Leftrightarrow & \color{red}{-1035} x& = & 236 \\\Leftrightarrow & x = \frac{236}{-1035} & & \\\Leftrightarrow & x = \frac{-236}{1035} & & \\ & V = \left\{ \frac{-236}{1035} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{2}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 30x-\frac{12}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x- \frac{60}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{-60} & = & \color{red}{-245x} +42 \\\Leftrightarrow & 1050x \color{red}{-60} \color{blue}{+60} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{+60} \\\Leftrightarrow & 1050x+245x& = & 42+60 \\\Leftrightarrow & \color{red}{1295} x& = & 102 \\\Leftrightarrow & x = \frac{102}{1295} & & \\ & V = \left\{ \frac{102}{1295} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{3})& = & -7x+\frac{4}{7} \\\Leftrightarrow & 12x+\frac{20}{3}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+140} & = & \color{red}{-147x} +12 \\\Leftrightarrow & 252x \color{red}{+140} \color{blue}{-140} \color{blue}{+147x} & = & \color{red}{-147x} +12 \color{blue}{+147x} \color{blue}{-140} \\\Leftrightarrow & 252x+147x& = & 12-140 \\\Leftrightarrow & \color{red}{399} x& = & -128 \\\Leftrightarrow & x = \frac{-128}{399} & & \\ & V = \left\{ \frac{-128}{399} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{3}{7})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 15x+\frac{15}{7}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x+ \frac{15}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{+15} & = & \color{red}{-49x} +6 \\\Leftrightarrow & 105x \color{red}{+15} \color{blue}{-15} \color{blue}{+49x} & = & \color{red}{-49x} +6 \color{blue}{+49x} \color{blue}{-15} \\\Leftrightarrow & 105x+49x& = & 6-15 \\\Leftrightarrow & \color{red}{154} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{154} & & \\ & V = \left\{ \frac{-9}{154} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{2}{5})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -18x-\frac{12}{5}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{-36} & = & \color{red}{-45x} +40 \\\Leftrightarrow & -270x \color{red}{-36} \color{blue}{+36} \color{blue}{+45x} & = & \color{red}{-45x} +40 \color{blue}{+45x} \color{blue}{+36} \\\Leftrightarrow & -270x+45x& = & 40+36 \\\Leftrightarrow & \color{red}{-225} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-225} & & \\\Leftrightarrow & x = \frac{-76}{225} & & \\ & V = \left\{ \frac{-76}{225} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & 3x+\frac{8}{5} \\\Leftrightarrow & 4x-\frac{6}{7}& = & 3x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-30} & = & \color{red}{105x} +56 \\\Leftrightarrow & 140x \color{red}{-30} \color{blue}{+30} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{+30} \\\Leftrightarrow & 140x-105x& = & 56+30 \\\Leftrightarrow & \color{red}{35} x& = & 86 \\\Leftrightarrow & x = \frac{86}{35} & & \\ & V = \left\{ \frac{86}{35} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{2}{3})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 16x-\frac{8}{3}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{48}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 48x \color{red}{-8} & = & \color{red}{21x} +4 \\\Leftrightarrow & 48x \color{red}{-8} \color{blue}{+8} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{+8} \\\Leftrightarrow & 48x-21x& = & 4+8 \\\Leftrightarrow & \color{red}{27} x& = & 12 \\\Leftrightarrow & x = \frac{12}{27} & & \\\Leftrightarrow & x = \frac{4}{9} & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)