Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{11})& = & 7x+\frac{7}{5} \\\Leftrightarrow & 12x-\frac{12}{11}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-60} & = & \color{red}{385x} +77 \\\Leftrightarrow & 660x \color{red}{-60} \color{blue}{+60} \color{blue}{-385x} & = & \color{red}{385x} +77 \color{blue}{-385x} \color{blue}{+60} \\\Leftrightarrow & 660x-385x& = & 77+60 \\\Leftrightarrow & \color{red}{275} x& = & 137 \\\Leftrightarrow & x = \frac{137}{275} & & \\ & V = \left\{ \frac{137}{275} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{3}{2})& = & -3x+\frac{2}{9} \\\Leftrightarrow & 25x-\frac{15}{2}& = & -3x+\frac{2}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{450}{ \color{blue}{18} }x- \frac{135}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{4}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 450x \color{red}{-135} & = & \color{red}{-54x} +4 \\\Leftrightarrow & 450x \color{red}{-135} \color{blue}{+135} \color{blue}{+54x} & = & \color{red}{-54x} +4 \color{blue}{+54x} \color{blue}{+135} \\\Leftrightarrow & 450x+54x& = & 4+135 \\\Leftrightarrow & \color{red}{504} x& = & 139 \\\Leftrightarrow & x = \frac{139}{504} & & \\ & V = \left\{ \frac{139}{504} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{2}{7})& = & -2x+\frac{2}{11} \\\Leftrightarrow & 15x+\frac{6}{7}& = & -2x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-154}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{+66} & = & \color{red}{-154x} +14 \\\Leftrightarrow & 1155x \color{red}{+66} \color{blue}{-66} \color{blue}{+154x} & = & \color{red}{-154x} +14 \color{blue}{+154x} \color{blue}{-66} \\\Leftrightarrow & 1155x+154x& = & 14-66 \\\Leftrightarrow & \color{red}{1309} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{1309} & & \\ & V = \left\{ \frac{-52}{1309} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{5}{2})& = & 5x+\frac{4}{11} \\\Leftrightarrow & 6x-\frac{15}{2}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{132}{ \color{blue}{22} }x- \frac{165}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{8}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 132x \color{red}{-165} & = & \color{red}{110x} +8 \\\Leftrightarrow & 132x \color{red}{-165} \color{blue}{+165} \color{blue}{-110x} & = & \color{red}{110x} +8 \color{blue}{-110x} \color{blue}{+165} \\\Leftrightarrow & 132x-110x& = & 8+165 \\\Leftrightarrow & \color{red}{22} x& = & 173 \\\Leftrightarrow & x = \frac{173}{22} & & \\ & V = \left\{ \frac{173}{22} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{3}{8})& = & -8x+\frac{4}{7} \\\Leftrightarrow & -21x-\frac{21}{8}& = & -8x+\frac{4}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1176}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{-448}{ \color{blue}{56} }x+ \frac{32}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1176x \color{red}{-147} & = & \color{red}{-448x} +32 \\\Leftrightarrow & -1176x \color{red}{-147} \color{blue}{+147} \color{blue}{+448x} & = & \color{red}{-448x} +32 \color{blue}{+448x} \color{blue}{+147} \\\Leftrightarrow & -1176x+448x& = & 32+147 \\\Leftrightarrow & \color{red}{-728} x& = & 179 \\\Leftrightarrow & x = \frac{179}{-728} & & \\\Leftrightarrow & x = \frac{-179}{728} & & \\ & V = \left\{ \frac{-179}{728} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{4}{3})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 8x-\frac{16}{3}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{96}{ \color{blue}{12} }x- \frac{64}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 96x \color{red}{-64} & = & \color{red}{-60x} +27 \\\Leftrightarrow & 96x \color{red}{-64} \color{blue}{+64} \color{blue}{+60x} & = & \color{red}{-60x} +27 \color{blue}{+60x} \color{blue}{+64} \\\Leftrightarrow & 96x+60x& = & 27+64 \\\Leftrightarrow & \color{red}{156} x& = & 91 \\\Leftrightarrow & x = \frac{91}{156} & & \\\Leftrightarrow & x = \frac{7}{12} & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{3}{5})& = & -7x+\frac{7}{4} \\\Leftrightarrow & -6x+\frac{9}{5}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-120}{ \color{blue}{20} }x+ \frac{36}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -120x \color{red}{+36} & = & \color{red}{-140x} +35 \\\Leftrightarrow & -120x \color{red}{+36} \color{blue}{-36} \color{blue}{+140x} & = & \color{red}{-140x} +35 \color{blue}{+140x} \color{blue}{-36} \\\Leftrightarrow & -120x+140x& = & 35-36 \\\Leftrightarrow & \color{red}{20} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{20} & & \\ & V = \left\{ \frac{-1}{20} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{4}{3})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -10x+\frac{8}{3}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{+16} & = & \color{red}{-42x} +27 \\\Leftrightarrow & -60x \color{red}{+16} \color{blue}{-16} \color{blue}{+42x} & = & \color{red}{-42x} +27 \color{blue}{+42x} \color{blue}{-16} \\\Leftrightarrow & -60x+42x& = & 27-16 \\\Leftrightarrow & \color{red}{-18} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-18} & & \\\Leftrightarrow & x = \frac{-11}{18} & & \\ & V = \left\{ \frac{-11}{18} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{3})& = & 9x+\frac{2}{5} \\\Leftrightarrow & 20x+\frac{16}{3}& = & 9x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x+ \frac{80}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{+80} & = & \color{red}{135x} +6 \\\Leftrightarrow & 300x \color{red}{+80} \color{blue}{-80} \color{blue}{-135x} & = & \color{red}{135x} +6 \color{blue}{-135x} \color{blue}{-80} \\\Leftrightarrow & 300x-135x& = & 6-80 \\\Leftrightarrow & \color{red}{165} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{165} & & \\ & V = \left\{ \frac{-74}{165} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{5}{8})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 6x+\frac{15}{8}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{336}{ \color{blue}{56} }x+ \frac{105}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{16}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 336x \color{red}{+105} & = & \color{red}{280x} +16 \\\Leftrightarrow & 336x \color{red}{+105} \color{blue}{-105} \color{blue}{-280x} & = & \color{red}{280x} +16 \color{blue}{-280x} \color{blue}{-105} \\\Leftrightarrow & 336x-280x& = & 16-105 \\\Leftrightarrow & \color{red}{56} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{56} & & \\ & V = \left\{ \frac{-89}{56} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{2}{11})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -10x+\frac{10}{11}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-110}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -110x \color{red}{+10} & = & \color{red}{77x} +8 \\\Leftrightarrow & -110x \color{red}{+10} \color{blue}{-10} \color{blue}{-77x} & = & \color{red}{77x} +8 \color{blue}{-77x} \color{blue}{-10} \\\Leftrightarrow & -110x-77x& = & 8-10 \\\Leftrightarrow & \color{red}{-187} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-187} & & \\\Leftrightarrow & x = \frac{2}{187} & & \\ & V = \left\{ \frac{2}{187} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{5}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{+50} & = & \color{red}{-245x} +42 \\\Leftrightarrow & -350x \color{red}{+50} \color{blue}{-50} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{-50} \\\Leftrightarrow & -350x+245x& = & 42-50 \\\Leftrightarrow & \color{red}{-105} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-105} & & \\\Leftrightarrow & x = \frac{8}{105} & & \\ & V = \left\{ \frac{8}{105} \right\} & \\\end{align}\)