Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{9})& = & -3x+\frac{3}{4} \\\Leftrightarrow & -14x+\frac{14}{9}& = & -3x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-504}{ \color{blue}{36} }x+ \frac{56}{ \color{blue}{36} })& = & (\frac{-108}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -504x \color{red}{+56} & = & \color{red}{-108x} +27 \\\Leftrightarrow & -504x \color{red}{+56} \color{blue}{-56} \color{blue}{+108x} & = & \color{red}{-108x} +27 \color{blue}{+108x} \color{blue}{-56} \\\Leftrightarrow & -504x+108x& = & 27-56 \\\Leftrightarrow & \color{red}{-396} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-396} & & \\\Leftrightarrow & x = \frac{29}{396} & & \\ & V = \left\{ \frac{29}{396} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{2}{3})& = & -3x+\frac{10}{9} \\\Leftrightarrow & 28x-\frac{14}{3}& = & -3x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{252}{ \color{blue}{9} }x- \frac{42}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 252x \color{red}{-42} & = & \color{red}{-27x} +10 \\\Leftrightarrow & 252x \color{red}{-42} \color{blue}{+42} \color{blue}{+27x} & = & \color{red}{-27x} +10 \color{blue}{+27x} \color{blue}{+42} \\\Leftrightarrow & 252x+27x& = & 10+42 \\\Leftrightarrow & \color{red}{279} x& = & 52 \\\Leftrightarrow & x = \frac{52}{279} & & \\ & V = \left\{ \frac{52}{279} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{2}{5})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -30x+\frac{12}{5}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-150}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -150x \color{red}{+12} & = & \color{red}{-35x} +2 \\\Leftrightarrow & -150x \color{red}{+12} \color{blue}{-12} \color{blue}{+35x} & = & \color{red}{-35x} +2 \color{blue}{+35x} \color{blue}{-12} \\\Leftrightarrow & -150x+35x& = & 2-12 \\\Leftrightarrow & \color{red}{-115} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-115} & & \\\Leftrightarrow & x = \frac{2}{23} & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-2)& = & 3x+\frac{4}{11} \\\Leftrightarrow & -14x+14& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 1 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-154}{ \color{blue}{11} }x+ \frac{154}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -154x \color{red}{+154} & = & \color{red}{33x} +4 \\\Leftrightarrow & -154x \color{red}{+154} \color{blue}{-154} \color{blue}{-33x} & = & \color{red}{33x} +4 \color{blue}{-33x} \color{blue}{-154} \\\Leftrightarrow & -154x-33x& = & 4-154 \\\Leftrightarrow & \color{red}{-187} x& = & -150 \\\Leftrightarrow & x = \frac{-150}{-187} & & \\\Leftrightarrow & x = \frac{150}{187} & & \\ & V = \left\{ \frac{150}{187} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{2}{9})& = & -8x+\frac{4}{11} \\\Leftrightarrow & 35x+\frac{14}{9}& = & -8x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{3465}{ \color{blue}{99} }x+ \frac{154}{ \color{blue}{99} })& = & (\frac{-792}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 3465x \color{red}{+154} & = & \color{red}{-792x} +36 \\\Leftrightarrow & 3465x \color{red}{+154} \color{blue}{-154} \color{blue}{+792x} & = & \color{red}{-792x} +36 \color{blue}{+792x} \color{blue}{-154} \\\Leftrightarrow & 3465x+792x& = & 36-154 \\\Leftrightarrow & \color{red}{4257} x& = & -118 \\\Leftrightarrow & x = \frac{-118}{4257} & & \\ & V = \left\{ \frac{-118}{4257} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{7})& = & 9x+\frac{10}{7} \\\Leftrightarrow & -18x-\frac{30}{7}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-126}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{63}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -126x \color{red}{-30} & = & \color{red}{63x} +10 \\\Leftrightarrow & -126x \color{red}{-30} \color{blue}{+30} \color{blue}{-63x} & = & \color{red}{63x} +10 \color{blue}{-63x} \color{blue}{+30} \\\Leftrightarrow & -126x-63x& = & 10+30 \\\Leftrightarrow & \color{red}{-189} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-189} & & \\\Leftrightarrow & x = \frac{-40}{189} & & \\ & V = \left\{ \frac{-40}{189} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{7})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -30x+\frac{18}{7}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-1260}{ \color{blue}{42} }x+ \frac{108}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -1260x \color{red}{+108} & = & \color{red}{294x} +35 \\\Leftrightarrow & -1260x \color{red}{+108} \color{blue}{-108} \color{blue}{-294x} & = & \color{red}{294x} +35 \color{blue}{-294x} \color{blue}{-108} \\\Leftrightarrow & -1260x-294x& = & 35-108 \\\Leftrightarrow & \color{red}{-1554} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-1554} & & \\\Leftrightarrow & x = \frac{73}{1554} & & \\ & V = \left\{ \frac{73}{1554} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{7})& = & 5x+\frac{7}{2} \\\Leftrightarrow & 12x-\frac{30}{7}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{-60} & = & \color{red}{70x} +49 \\\Leftrightarrow & 168x \color{red}{-60} \color{blue}{+60} \color{blue}{-70x} & = & \color{red}{70x} +49 \color{blue}{-70x} \color{blue}{+60} \\\Leftrightarrow & 168x-70x& = & 49+60 \\\Leftrightarrow & \color{red}{98} x& = & 109 \\\Leftrightarrow & x = \frac{109}{98} & & \\ & V = \left\{ \frac{109}{98} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{7})& = & -9x+\frac{2}{5} \\\Leftrightarrow & -20x-\frac{10}{7}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{-50} & = & \color{red}{-315x} +14 \\\Leftrightarrow & -700x \color{red}{-50} \color{blue}{+50} \color{blue}{+315x} & = & \color{red}{-315x} +14 \color{blue}{+315x} \color{blue}{+50} \\\Leftrightarrow & -700x+315x& = & 14+50 \\\Leftrightarrow & \color{red}{-385} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-385} & & \\\Leftrightarrow & x = \frac{-64}{385} & & \\ & V = \left\{ \frac{-64}{385} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{4})& = & 2x+\frac{10}{3} \\\Leftrightarrow & -28x+\frac{21}{4}& = & 2x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-336}{ \color{blue}{12} }x+ \frac{63}{ \color{blue}{12} })& = & (\frac{24}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -336x \color{red}{+63} & = & \color{red}{24x} +40 \\\Leftrightarrow & -336x \color{red}{+63} \color{blue}{-63} \color{blue}{-24x} & = & \color{red}{24x} +40 \color{blue}{-24x} \color{blue}{-63} \\\Leftrightarrow & -336x-24x& = & 40-63 \\\Leftrightarrow & \color{red}{-360} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-360} & & \\\Leftrightarrow & x = \frac{23}{360} & & \\ & V = \left\{ \frac{23}{360} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{4}{5})& = & -4x+\frac{10}{3} \\\Leftrightarrow & 9x+\frac{12}{5}& = & -4x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-60}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{+36} & = & \color{red}{-60x} +50 \\\Leftrightarrow & 135x \color{red}{+36} \color{blue}{-36} \color{blue}{+60x} & = & \color{red}{-60x} +50 \color{blue}{+60x} \color{blue}{-36} \\\Leftrightarrow & 135x+60x& = & 50-36 \\\Leftrightarrow & \color{red}{195} x& = & 14 \\\Leftrightarrow & x = \frac{14}{195} & & \\ & V = \left\{ \frac{14}{195} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{11})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -10x+\frac{10}{11}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-110}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -110x \color{red}{+10} & = & \color{red}{-77x} +4 \\\Leftrightarrow & -110x \color{red}{+10} \color{blue}{-10} \color{blue}{+77x} & = & \color{red}{-77x} +4 \color{blue}{+77x} \color{blue}{-10} \\\Leftrightarrow & -110x+77x& = & 4-10 \\\Leftrightarrow & \color{red}{-33} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-33} & & \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)